Radiation, temperature, and vacuum effectson piezoelectric wafer active sensors

Victor Giurgiutiu1, Cristian Postolache2 and Mihai Tudose3

1University of South Carolina, Columbia, South Carolina, USA2National Institute for Physics and Nuclear Engineering IFIN, Bucharest, Romania3National Institute of Aerospace Research INCAS, Bucharest, Romania

E-mail: victorg@sc.edu

Received 1 June 2015, revised 11 November 2015Accepted for publication 15 January 2016Published 22 February 2016

AbstractThe effect of radiation, temperature, and vacuum (RTV) on piezoelectric wafer active sensors(PWASs) is discussed. This study is relevant for extending structural health monitoring (SHM)methods to space vehicle applications that are likely to be subjected to harsh environmentalconditions such as extreme temperatures (hot and cold), cosmic radiation, and interplanetaryvacuums. This study contains both theoretical and experimental investigations with the use ofelectromechanical impedance spectroscopy (EMIS). In the theoretical part, analytical models ofcircular PWAS resonators were used to derive analytical expressions for the temperaturesensitivities of EMIS resonance and antiresonance behavior. Closed-form expressions forfrequency and peak values at resonance and antiresonance were derived as functions of thecoefficients of thermal expansion, a a a, , ;1 2 3 the Poisson ratio, n and its sensitivity, n¶ ¶T;the relative compliance gradient ¶ ¶s T s ;E E

11 11( ) and the Bessel function root, z and itssensitivity, ¶ ¶z T . In the experimental part, tests were conducted to subject the PWAStransducers to RTV conditions. In one set of experiments, several RTV exposure, cycles wereapplied with EMIS signatures recorded at the beginning and after each of the repeated cycles. Inanother set of experiments, PWAS transducers were subjected to various temperatures and theEMIS signatures were recorded at each temperature after stabilization. The processing ofmeasured EMIS data from the first set of experiments revealed that the resonance andantiresonance frequencies changed by less than 1% due to RTV exposure, whereas the resonanceand antiresonance amplitudes changed by around 15%. After processing an individual set ofEMIS data from the second set of experiments, it was determined that the relative temperaturesensitivity of the antiresonance frequency ( f fAR AR ) is approximately ´ -63.1 10 C6 and therelative temperature sensitivity of the antiresonance amplitude (ReZ) is approximately

´ -3.31 10 C.3 A tentative statistical analysis and comparative plots of the data from sets ofPWAS transducers revealed that the trends observed on an individual PWAS are also observedon the entire set of PWAS transducers. The article concludes with a summary, conclusions, andsuggestions for further work.

Keywords: structural health monitoring, piezoelectric wafer active sensors, radiation effects,temperature effects, vacuum effects, SHM, PWAS

(Some figures may appear in colour only in the online journal)

1. Introduction

The motivation for this article is the need for transitioningstructural health monitoring (SHM) methodology to space-vehicle applications. So far, SHM research has been focused

on aeronautical applications, however, the need for SHM alsoexists in space-vehicle applications. Notwithstanding, thechallenges posed by operating in the outer space are muchgreater than those posed by operating in the Earth’s atmos-phere. A space vehicle is subjected to large temperature

Smart Materials and Structures

Smart Mater. Struct. 25 (2016) 035024 (25pp) doi:10.1088/0964-1726/25/3/035024

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excursions as it moves from the heat of direct sunlight to thecoldness of Earth’s penumbra. The space environment is alsosubject to cosmic rays that may impose significant radiationeffects. In addition, everything in space is enclosed in anadvanced vacuum, which may affect materials containingvolatile compounds. For these reasons, the need exists forstudying the effect of space-environment conditions on SHMsystems.

1.1. State of the art

SHM can be performed in two main ways: (a) passive SHM;and (b) active SHM. Passive SHM is mainly concerned withmeasuring various operational parameters and inferring thestate of structural health from the analysis of these parameters.For example, one could monitor the flight parameters of anaircraft (airspeed, air turbulence, g-factors, vibration levels,stresses in critical locations, etc) and then use the aircraftdesign algorithms to infer how much of the aircraft’s usefullife has been used up and how much is expected to remain.Passive SHM is useful, but it does not directly address thecrux of the problem, (i.e., it does not directly examine if thestructure has been damaged or not). In contrast, active SHM isconcerned with directly assessing the state of structural healthby trying to detect the presence and extent of structuraldamage. In this respect, the active SHM approach is similarwith the approach taken in non-destructive evaluation meth-odologies, only that active SHM takes it one-step further:active SHM attempts to develop damage detection sensorsthat can be permanently installed on the structure and mon-itoring methods that can provide an on demand structuralhealth bulletin.

1.1.1. Piezoelectric wafer active sensors (PWASs). PWASsare small, lightweight, inexpensive transducers that can bebonded onto the structural surface, can be mounted insidebuilt–up structures, and can be even embedded betweenthe structural and non-structural layers of a completeconstruction. Studies are also being performed onembedding PWAS between the structural layers ofcomposite materials, though the associated issues ofcomposites durability and damage tolerance has still to beovercome. PWAS transducers can serve several purposes [1]:(a) high-bandwidth strain sensors; (b) high-bandwidth waveexciters and receivers; (c) resonators; or (d) embedded modalsensors with the EMIS method. By application types, PWAStransducers can be used for (i) active sensing of far-fielddamage using pulse-echo, pitch-catch and phased-arraymethods, (ii) active sensing of near-field damage usinghigh-frequency E/M impedance method and thickness-gagemode, and (iii) passive sensing of damage-generating eventsthrough detection of low-velocity impacts and acousticemission at the tip of advancing cracks (figure 1). PWASphased arrays permit broadside and offside cracks to beindependently identified with scanning beams emitting from acentral location. The main advantage of PWAS overconventional ultrasonic probes lies in their small size,lightweight design, low profile, and modest cost. In spite of

their small size, PWAS have been shown to be able toreplicate many of the functions performed by conventionalultrasonic probes such as pitch-catch, pulse-echo, phased-arrays, etc [1].

1.1.2. Previous work1.1.2.1. Temperature effects. Several previous studies haveexamined the effect of temperature on common piezoceramicmaterials and transducers. Hooker [2] studied the variation ofpiezoelectric properties with temperature in the range−150 °C to +250 °C for several PZT piezoceramicformulations. It was found that the basic piezoelectricconstants vary monotonically away from the Curietemperature, but their behavior changes rapidly closer to theCurie temperature. For commonly used piezoceramics, theCurie temperature varies around 300 °C. Beyond the Curietemperature, piezoceramics lose their piezoelectric properties.This means that a piezoelectric-based SHM system wouldlose its functionality at elevated temperatures beyond theCurie temperature. For practical applications, a stand-offdistance below the Curie temperature must be consideredand operation should be restricted to temperatures less than175–200 °C [3, 4]. The effect of temperature change onPWAS EMIS signature was studied in the 29–59 °C range byBastani et al [5]; it was found that frequency and magnitudeof the impedance real-part plots (ReZ) decreasedmonotonically with the increase in temperature. Similareffects were reported in the 25–100 °C range by Baptistaet al [6].

Piezoceramics should remain functional at all tempera-tures below the Curie temperature, but their behavior may beaffected by the cryogenic regime, as indicated by Hooker [2].Paik et al [7] developed specialty piezoceramic formulationsto operate at cryogenic temperatures. Qing et al [8] performedliquid nitrogen tests and showed that piezoelectric-sensor-based SHM systems can be operated satisfactory at −196 °Ccryogenic temperature.

An experimental study of PWAS performance at bothcryogenic and elevated temperatures were conducted by Linet al [9]. It was found that PWAS resonators maintain theiroperability at −196 °C cryogenic temperature and regain theiroriginal behavior after return to room temperature. They alsofound that the PWAS resonators with Curie temperature of330 °C maintain their original behavior after exposure toelevated temperatures up to 200 °C. Exposure to highertemperatures (e.g., 260 °C) had a degrading effect on thebehavior measured upon return to room temperature. Thepiezoelectric functionality was found to strongly degrade andthen disappear completely after exposure to even greatertemperatures (315 °C and 370 °C, respectively).

The temperature range expected in lower Earth orbit(LEO) could vary from −125 °C to 150 °C. Furthermore, theactual temperatures in the void space can be as low as−270 °C. Despite these extreme temperatures, the previousstudies [2] through [9] discussed above seem to indicate thatconventional PZT material may be able to survive space-operation conditions.

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Smart Mater. Struct. 25 (2016) 035024 V Giurgiutiu et al

1.1.2.2. Radiation effects. In an early study, Broomfield [10]examined the effect of low-fluence neutron irradiation onsilver-electrode piezoelectric ceramics and found thatirradiation increased the thickness-mode resonantfrequencies and decreased the elevated temperatureelectromechanical coupling. This effect was attributed toreduction in the piezoceramic polarization and changes in thebonding of the silver electrode.

More recently, Lin et al [11] performed irradiationexposure experiments on PWAS resonators. The absorbeddose ranged from 3 to 50Mrad (30–500 kGy) where a Co-60gamma source with a maximum dose rate of 2.5 Mrad h−1

(25 kGy h−1) was used. The absorbed dose rate wascalculated to be approx. 1.55 MRad h−1 (15.5 kGy h−1) withexposure times of 2, 4, and 8 h. EMIS measurements weretaken for in-plane and out-of-plane (thickness-mode) vibra-tion. Free and wired PWAS resonators were used. Thisexploratory work showed that the PWAS survived well theirradiation and successfully maintained their functionality.Some changes in the EMIS spectrum were observed,especially for the wired PWAS resonators. These changesconsisted in slight spectrum shifts towards higher frequenciesand higher impedance values. It was also observed thatirradiation decreased the electrical capacitance measured witha standard multimeter instrument. As suggested by Broom-field [10], the observed effects were attributed to a change inthe electrode bonding and a reduction in the polarization ofthe ceramic.

An even more recent study of radiation effects onpiezoelectric materials was presented by Parks and Tittmannin 2014 [12]. The study was done on piezoelectric single-

crystal aluminum nitride (AlN) that was considered as apossible candidate material for ultrasonic transducers used innuclear reactors. The radiation tolerance of this piezoelectricmaterial was demonstrated first through thermal neutronexposure and gamma irradiation. This radiation tolerance ofaluminum nitride, coupled with its known temperaturestability, makes it an ideal candidate for acoustic emissionused in very harsh radiation/temperature conditions, whichare typical of nuclear reactor applications.

1.1.2.3. Vacuum effects. A cursory investigation ofspecialized literature revealed no references or studies of thevacuum effects on piezoceramics. This is not surprising sincethe ceramic itself is a stable compound unlikely to be affectedby vacuum presence. (In contrast, piezopolymers may beaffected by outgassing in vacuum; however, piezopolymersare considered in the present investigation.)

An interesting effect that might appear while exciting apiezoceramic at reduced environmental pressures would bethat of glow discharge (corona effect) which could produce ashortening path between the electrodes in the 0.01–10 Torrpressure range. Since outer space vacuum is below0.000 001 Torr, the corona discharge effect need not be ofconcern in this article.

1.2. About the present article

This article presents a combined theoretical-experimentalapproach to understanding the effects that radiation, temper-ature, and vacuum (RTV) have on the performance of PWAStransducers for potential transition of SHM methods to space-vehicle applications. Our approach is aligned with the need to

Figure 1. Use of piezoelectric wafer active sensors (PWAS) as traveling wave and standing wave transducers for damage detection in thin-wall structures [1]. Reproduced with permission from Elsevier.

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Smart Mater. Struct. 25 (2016) 035024 V Giurgiutiu et al

answer three questions: (a) can the PWAS transducers surviveexposure to simulated space-environment conditions? (b) Ifthey survive, how will their performance be affected? (c) Ifthe performance is affected, what will be the sensitivitycoefficients that could be considered in predicting the func-tionality of PWAS transducers under space-environmentconditions?

The main investigative method used in our study is theEMIS. To keep the number of variables manageable, wefocused this article on the PWAS transducer itself, i.e., westudied the behavior of a free PWAS resonator not attached toa structure. In this way, we can establish how the behavior ofthe transducer is affected by the simulated space environment.

The piezoelectric material discussed in this article is acommercially available lead zirconate (PZT) that is relativelyinexpensive and hence widely used in active SHM studies.The properties of this soft PZT material are close to those ofAmerican Piezoceramics Corp. designation APC-850. Ourchoice of this soft piezoelectric material was based on (a)availability, (b) good wave-transmission capability; (c) rea-sonable wave-reception sensitivity, and (d) affordability.Admittedly, this soft PZT formulation would not be applic-able for very harsh temperature–radiation conditions as foundin a nuclear reactor but it seems that it might survive therelatively milder temperature–radiation conditions encoun-tered in space vehicle applications.

The behavior of PWAS transducers adhesively attachedto structural elements and the evaluation of their capability todetect structural damage under simulated space-environmentconditions make the object of a separate communication andare not discussed here.

2. Theory

In this section, the theoretical model of the PWAS resonatorwill be briefly reviewed. Subsequently, the sensitivity of thismodel to various modeling parameters will be investigated.The study will be extended to include the dependence ofcertain modeling parameters on the environmental conditionsof interest including (a) temperature, and (b) radiation expo-sure. (Vacuum effects will not be included in the model since,as shown in section 1.1.2, vacuum is unlikely to affect thepiezoceramic behavior.) Finally, the conceptual conclusionsdrawn for a free PWAS resonator will be extended to the caseof a constrained PWAS resonator, specifically the modelingof PWAS EMIS for a circular plate with a PWAS transducerattached in its center.

2.1. Theoretical model of a PWAS resonator; E/M impedancespectrum; resonance frequencies and peak amplitudes of theimpedance real part

Consider a circular PWAS transducer of radius a, andthickness t (figure 2). The PWAS is made of thickness-polarized piezoelectric material while the top and bottomsurfaces are covered with conducting electrodes. The PWASis assumed to undergo in-plane expansion and contraction

under the effect of an oscillating electric field, E ,3 applied tothe top and bottom electrodes.

The electric field is produced through application of aharmonic voltage = wV t V e ti( ) ˆ between the top and bottomelectrodes. The resulting electric field is assumed uniformover the electrode’s area. Because the electric field is uniform,the response will be assumed to be axially symmetric mean-ing that the circular piezoelectric wafer undergoes uniformradial and circumferential expansion. The motion is time-harmonic with an angular frequency, w. To keep notationssimple, only the space dependency is considered, i.e., alldependent variables are assumed to be the complex ampli-tudes of their time oscillations (e.g., when we write u weactually mean u .ˆ ) The ‘uniform electric field’ assumptionimplies that the derivative with respect to q is zero (i.e.,

q¶ ⋅ ¶ =/ 0( ) ) and that the circumferential displacement isalso zero (i.e., =qu 0).

2.1.1. Electromechanical admittance and impedance. Underthese assumptions, the electromechanical (E/M) admittanceand impedance of the PWAS resonator can be expressed as

w w

nn

=

´ - -+- -

/

⎡⎣⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥

Y C

kJ z

zJ z J z

i

1 11

1

E M admittance , 1

p2 1

0 1

¯ ( ) ¯

¯ ( ) ( ¯)¯ ( ¯) ( ) ( ¯)

( ) ( )

ww

nn

=

´ - -+- -

-

/

⎡⎣⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥

ZC

kJ z

zJ z J z

1

i

1 11

1

E M impedance , 2

p2 1

0 1

1

¯ ( ) ¯

¯ ( ) ( ¯)¯ ( ¯) ( ) ( ¯)

( ) ( )

where J z0 ( ) and J z1( ) are the Bessel functions of order 0 and1, w is the angular frequency, and the other variables andparameters are described as follows. The full derivation ofthese relations is given in [1] and needs not be repeated here.Nonetheless, some clarifications about the meaning of theintervening variables and parameters are warranted. Theparameter kp¯ is the planar electromechanical coupling factorof the piezoelectric material given by

n e=

-k

d

s

2

1

planar electromechanical coupling coefficient , 3

p E T2 31

2

11 33

¯( ) ¯ ¯

( ) ( )

Figure 2. Circular PWAS resonator.

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Smart Mater. Struct. 25 (2016) 035024 V Giurgiutiu et al

where n is the Poisson ratio of the piezoelectric material ands E11 is the in-plane compliance of the piezoelectric material andsignifies the in-plane strain per unit in-plane stress. Thecoefficient eT

33 is the transverse electric permittivity of thepiezoelectric material and signifies the transverse electricdisplacement induced by a transverse electric field of unitmagnitude. The coefficient d31 signifies the coupling betweenthe electrical and the mechanical variables, i.e., the charge perunit stress or the strain per unit electric field. Typical values ofthese constants are given in table 1.

The variable C is the electrical capacitance of the PWAStransducer under free boundary conditions; the value of C iscalculated with the following formula:

ep

=Ca

tfree electrical capacitance . 4T

33

2¯ ¯ ( ) ( )

The parameter cp¯ is the planar wave speed of thepiezoelectric material given by

r n=

-c

s

1

1planar wave speed , 5

Ep11

2¯

¯ ( )( ) ( )

where r is the density of the piezoelectric material. Thevariable z is a non-dimensional variable defined by the ratiobetween the angular frequency multiplied with the disc radiusand divided by the wave speed, as shown below

w=z a c 6p¯ ¯ ( )

The damping effects in the piezoelectric material arecovered through the adoption of mechanical and electricaldissipation parameters, η and ξ, that lead to complexexpressions for compliance and dielectric permittivity, i.e.

h e e x= - = -s s 1 i , 1 i . 7E E T11 11 33 33¯ ( ) ¯ ( ) ( )

The values of η and x are usually small (h x <, 5%).

2.1.2. Resonance frequencies. If the frequency w of theexcitation electric voltage = wV t V e ti( ) ˆ is swept over a givenrange, the PWAS resonator will encounter the resonancephenomenon at certain resonance frequencies. As indicatedin [1], the resonance frequencies correspond to strongelectromechanical activity accompanied by large values ofthe electric current I drawn from the excitation source; inelectrical terms, this situation is interpreted as admittancepeaks given that = /Y I V .ˆ ˆ To simplify the analysis, let usconsider for the moment a non-dissipative model ofadmittance and impedance that yields

w w

nn

=

´ - -+- -

- /

⎡⎣⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥

Y C

kJ z

zJ z J z

i

1 11

1

non dissipative E M admittance , 8

p2 1

0 1

( )( ) ( )

( ) ( ) ( )( ) ( )

ww

nn

=

´ - -+- -

-

-

/

⎡⎣⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥

ZC

kJ z

zJ z J z

1

i

1 11

1

non dissipative E M impedance . 9

p2 1

0 1

1

( )

( ) ( )( ) ( ) ( )

( ) ( )

The condition for electromechanical resonance is obtainedby studying the poles of Y, i.e., the values of z that make ¥Y . The poles of Y are roots of the denominator of

equation (8), which is n- -zJ z J z1 .0 1( ) ( ) ( ) Hence, thevalues of z for resonance are obtained by solving the equation

n- - =zJ z J z1 0 resonance . 100 1( ) ( ) ( ) ( ) ( )

This equation is the same as the equation used todetermine the mechanical resonance of circular platesundergoing axisymmetric in-plane vibration [13]. This isnot surprising since the in-plane axisymmetric modes ofvibration couple well with a uniform electric field excitation.Hence, the frequencies of electromechanical resonancecorrespond identically to the frequencies for axisymmetricin-plane mechanical resonance. Equation (10) is a transcen-dental equation and its roots are found numerically andthe value of these roots changes if the Poisson ratio nchanges. A typical Poisson ratio value for piezoelectricceramics is =v 0.35; hence, equation (10) yields the roots(eigenvalues):

= = =

= ¼ =

z z z

z v

2.079 508; 5. 398 928; 8. 577 761;

11. 736 076 0.35 .

11

1 2 3

4 ( )( )

For every eigenvalue, z ,j the corresponding resonancefrequency is given by

wp

= = = ¼c

az f

c

az j

1

2, 1, 2, 3,

resonance frequencies . 12

jp

j jp

j

( ) ( )

Table 1. Typical properties of PWAS piezoelectric material(APC-850).

Property Symbol Value

Compliance, in plane s E11 15.30×10−12 Pa−1

Compliance, thickness wise s E33 17.30×10−12 Pa−1

Dielectric constant eT33 e e= 1750T

33 0

Thickness wise induced-straincoefficient

d33 400×10−12 m V−1

In-plane induced-straincoefficient

d31 −175×10−12 m V−1

Coupling factor, parallel toelectric field

k33 0.72

Coupling factor, transverse toelectric field

k31 0.36

Poisson ratio n 0.35Density r 7700 kg m−3

Sound speed c 2900 m s−1

Curie temperature TC 360 °C

Note: e = ´ - -8.85 10 Fm012 1.

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Smart Mater. Struct. 25 (2016) 035024 V Giurgiutiu et al

2.1.3. Antiresonance frequencies. The phenomenon ofantiresonance is defined as the antithesis of resonance, i.e.,when the current drawn from the excitation source isminimum. Thus the antiresonance corresponds to a verysmall admittance Y , and thus a very large impedance Z (since=Z Y1 .) The condition for electromechanical antiresonance

is obtained by studying the zeroes of Y or the values of zwhich make =Y 0. (These zeros of Y are poles of Z since=Z Y1 .) equation (8) indicates that =Y 0 when

nn

- -+- -

=⎛⎝⎜

⎞⎠⎟k

J z

zJ z J z1 1

1

10. 13p

2 1

0 1

( ) ( )( ) ( ) ( )

( )

Upon rearrangement of equation (13),

nn

= -+- -

⎛⎝⎜

⎞⎠⎟k

J z

zJ z J z1 1

1

1, 14p

2 1

0 1

( ) ( )( ) ( ) ( )

( )

Or

nn n

- - =

- - - +

zJ z J z k zJ z

J z J z

1

1 1 . 150 1 p

20

1 1

( ) ( ) ( ) ( ( )( ) ( ) ( ) ( )) ( )

Hence, the antiresonance condition is

n-

- -

-=

zJ z

J z

k

k

1 2

10 antiresonance . 160

1

p2

p2

( )( ) ( )

( ) ( )

This equation is also transcendental and does not acceptclosed-form solutions; again, its solutions are found numeri-cally and the value of these roots change if the Poisson ratio nchanges. Using =v 0.35 from before, equation (16) yieldsthe antiresonance roots (antiresonance eigenvalues):

= =

= = ¼ =

z z

z z v

2.499 247; 5.563 254;

8. 681 470; 11.811 941 0.35 .

17

1AR

2AR

3AR

4AR ( )

( )

For every antiresonance eigenvalue, z ,jAR the corresp-

onding antiresonance frequency is given by

wp

= = = ¼c

az f

c

az j

1

2, 1, 2, 3,

antiresonance frequencies . 18

jp

j jp

jAR AR AR AR

( ) ( )

2.1.4. Admittance and impedance spectra. The resonanceand antiresonance behavior is best examined by studying thereal parts of the admittance and impedance frequency spectra.Figure 3 presents the numerical simulation of admittance andimpedance response for a circular PWAS resonator;figure 3(a) shows the overlapped plots of the real andimaginary parts of the admittance wY ( ) and impedance wZ .( )Figure 3(b) shows the log-lin plot of the admittance andimpedance real parts. From figure 3(a), one sees that theadmittance and impedance real parts display peaks exactly atthe locations where their imaginary parts display a zigzag

behavior. These locations correspond to resonances andantiresonances, respectively. It is also apparent that thedominant response in the admittance imaginary part exhibitslinear growth with frequency; examination of equation (1)indicates that, outside resonances, the admittance can beapproximated with w~ Ci .¯ Similarly, equation (2) indicatesthat outside antiresonances, the impedance can beapproximated with w~ C1 i .¯ Hence, it is more difficult toidentify the resonance and antiresonance response in plots ofthe admittance and impedance imaginary parts than it is inplots of the real parts. For this reason, future discussion willbe focused on examining only plots of the admittance andimpedance real parts (‘real spectra’).

2.2. Sensitivity of the PWAS resonator model to modelingparameters

In this section, we will examine the sensitivity of the PWASresonator model described by equations (1) and (2) to themodeling parameters. The study will be extended to includethe dependence of these modeling parameters on the envir-onmental conditions of interest including (a) temperature, and(b) radiation exposure. We will start with studying the sen-sitivity of the resonance and antiresonance frequencies andfollow with the sensitivity of the peak amplitudes in theadmittance and impedance spectra.

2.2.1. Resonance frequency sensitivity to modelingparameters. To study the resonance frequency sensitivity,recall equation (12) and apply a Taylor series expansion interms of the parameters c ,p a, z, to get

dw d d d= + -a

z cc

az

c

az a

1. 19p

p p

2( )

Note that equation (19) applies to any frequency wj butthe index j has been omitted for the sake of clarity. Next, weexamine how the increments dc ,p dz, da depend on the basicmaterial properties. Recall equation (5) and write it as

r n= - -c s 1 . 20Ep 11

2 1 2[ ( )] ( )

Taylor series expansion of equation (20) yields

d r n

drr

d ndnn

drr

d ndnn

= - -

´ + --

= - + --

-

⎡⎣⎢

⎤⎦⎥

⎡⎣⎢

⎤⎦⎥

c s

s

s

cs

s

1

21

2

1

1

2

2

1. 21

E

E

E

E

E

p 112 1 2

11

112

p11

112

[ ( )]

( )

( )( )

Equation (21) shows the sensitivity of the piezoelectricmaterial planar wave speed cp to variation of the piezoelectricmaterial properties r, s ,E

11 and n .Next, we examine the sensitivity of the resonance

eigenvalue z to variation of the piezoelectric materialproperties. Recall that z is a root of equation (10) which is

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Smart Mater. Struct. 25 (2016) 035024 V Giurgiutiu et al

a transcendental equation. Examination of equation (10)reveals that the only intervening material property is thePoisson ratio n; however, the dependence of z on n cannot becalculated explicitly because equation (10) is a transcendentalequation. Hence, we write formally

dndn=z

zd

d, 22( )

where the sensitivity nzd d has to be determined numericallyby calculating and plotting the transcendental roots z over arange of n values.

Finally, we examine the sensitivity of a with respect tothe piezoelectric material properties. We notice that a isgeometric dimension and hence the only piezoelectricmaterial property that it might depend on would be the in-plane coefficient of thermal expansion a ;1 thus

d a d=a a T. 231 ( )

If expansion due to radiation exposure is also present, anadditional term depending on the radiation dose should alsobe added to equation (23).

The last step in the process is to determine the sensitivityof the material properties to environmental conditions, i.e., (a)temperature, T , and (b) radiation exposure dose, D. We willstart with the dependence on temperature, T , of thepiezoelectric material planar wave speed, c .p Examination ofequation (21) reveals that the intervening piezoelectricmaterial properties are r, s ,E

11 n. The density r depends ontemperature through the coefficients of thermal expansiona a a, , ,1 2 3 in the 1, 2, and 3 directions, respectively. Recallthat r = mass Vol and d a a a d» + + TVol Vol.1 2 3[( ) ]Applying chain differentiation, we write

ð24Þ

The temperature sensitivity of compliance s E11 and

Poisson ratio n are not readily expressible; hence we write

d d dnnd=

¶¶

=¶¶

ss

TT

TT, , 25E

E

1111 ( )

Figure 3. Simulated frequency spectra of admittance and impedance of a circular PWAS resonator ( = =d a2 6. 98 mm, =t 0.216 mm,a

= ´s 18 10 Pa ,E11

12 1– – = ´ -d 175 10 m V ,3112 1– – APC-850 piezoceramic, h x= = 1% :) (a) complete plots showing both real (full line)

and imaginary (dashed line) parts; (b) plots of real part only, log scale.

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Smart Mater. Struct. 25 (2016) 035024 V Giurgiutiu et al

where the sensitivities s Td ,E11 n Td d has to be determined

experimentally.Substitution of equations (24), (25) into equation (21)

yields

d a a a

nn

nd

= - - + + +¶¶

--

¶¶

⎡⎣⎢

⎤⎦⎥

c cs

s

T

TT

1

2

1

2

1. 26

p E

E

p 1 2 311

11

2

( )

( )( )

Substitution of equations (22), (23), (25) and (26) intoequation (19) gives

dw a a a

nn

nd

nnd a d

= - - + +

+¶¶

--

¶¶

+¶¶

-

⎤⎦⎥

⎫⎬⎭

az c

s

s

T TT

c

a

z

TT

c

az a T

1 1

2

1 2

1.

d

d27

E

E

p 1 2 3

11

112

p p

2 1

{ [ ( )

( )

( )

Upon rearrangement, equation (27) becomes

ð28Þ

or

dw a a a

nn

nn

na d

= + + -¶¶

+-

¶¶

+¶¶

-

⎡⎣⎢

⎤⎦⎥

c z

a s

s

T

T z

z

TT

1

2

1

2

12

1 d

d2 29

E

Ep

1 2 311

11

2 1

( )

( )( )

Substitution of equation (12) into equation (29) yields,upon rearrangement

dw w a a a

nn n

nd

= - + + -¶¶

+-

+¶¶

⎧⎨⎩⎡⎣⎢

⎤⎦⎥

⎫⎬⎭

s

s

T

z

z

TT

1

2

1

21

1 d

d30

E

E

1 2 311

11

2( )( )

or

dww

da a a

nn n

nd

= = - + + -¶¶

+-

+¶¶

⎧⎨⎩⎡⎣⎢

⎤⎦⎥

⎫⎬⎭

f

f s

s

T

z

z

TT

1

2

1

21

1 d

d31

E

E

1 2 311

11

2( )( )

i.e.

ww

a a a

nn n

n

¶ ¶=

¶ ¶= - + +

-¶¶

+-

+¶¶

⎡⎣⎢

⎤⎦⎥

⎫⎬⎭

T f T

f

s

s

T z

z

T

1

2

12

1

1 d

d. 32

E

E

1 2 3

11

112

{

( )( )

Equation (32) describes the relative temperature sensi-tivity of the resonance frequency, w, in terms of the modelingparameter’s sensitivities. A similar expression may be derivedfor the radiation sensitivity.

2.2.2. Antiresonance frequency sensitivity to modelingparameters. In order to discuss the antiresonancefrequency sensitivity to modeling parameters, we notice thatequations (17) and (12) are very similar and that the onlydifference between them is the selection of the appropriateeigenvalue, zj for the resonance frequency w ,j and zj

AR for the

antiresonance frequency w .jAR Hence, in order to adapt the

resonance frequency sensitivity expression in equation (32) tothe calculation of the relative antiresonance frequencysensitivity, we only need to replace nzd d with nzd dAR toobtain

ww

a a a

nn

nn

n

¶ ¶=

¶ ¶= - + +

-¶¶

+-

¶¶

+¶¶

⎡⎣⎢

⎤⎦⎥

⎫⎬⎭

T f T

f

s

s

T T z

z

T

1

2

1 2

1

2 d

d. 33

E

E

AR

AR

AR

AR 1 2 3

11

112

AR

{

( )( )

2.2.3. Sensitivity of the admittance peak amplitudes tomodeling parameters. To examine the sensitivity of theadmittance peak amplitudes to modeling parameters, recallequation (1) and evaluate it at the resonance frequencies (wj)corresponding to the poles of the non-dissipative admittancegiven from equation (8). This evaluation is a reasonableapproximation of the actual behavior for small dissipation(h x <, 5% .) Hence

w w

nn

=

´ - -+

- -

/

⎡⎣⎢⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥⎥

Y C

kJ z

z J z J z

i

1 11

1

E M admittance at resonance , 34

j j

j

j j jp2 1

0 1

¯ ( ) ¯

¯ ( ) ( ¯ )¯ ( ¯ ) ( ) ( ¯ )

( ) ( )

where w=z a c .j j p¯ ¯ Expansion of equation (34) yields

w wn

n

wn n

n

wn

wn

n

= ++- -

-

=

´ ++ - + -

- -

= +-

- -

=- + + -

- -

⎡⎣⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥

⎡⎣⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥

⎡⎣⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥

Y C kJ z

zJ z J z

C

kJ z zJ z J z

zJ z J z

C kJ z zJ z

zJ z J z

Ck J z k zJ z

zJ z J z

i 11

11

i

11 1

1

i 12

1

i2 1 1

1.

35

p

p2 1

0 1

p2 1 0 1

0 1

p2 1 0

0 1

p2

12

0

0 1

¯ ( ) ¯ ¯ ( ) ( ¯)¯ ( ¯) ( ) ( ¯)

¯

¯ ( ) ( ¯) ¯ ( ¯) ( ) ( ¯)¯ ( ¯) ( ) ( ¯)

¯ ¯ ( ¯) ¯ ( ¯)¯ ( ¯) ( ) ( ¯)

¯ ( ¯ ) ( ¯) ( ¯ ) ¯ ( ¯)¯ ( ¯) ( ) ( ¯)

( )

8

Smart Mater. Struct. 25 (2016) 035024 V Giurgiutiu et al

Note that the subscript j was omitted in equation (35) forsimplicity, but its presence is implied. For sensitivity analysis,we express the admittance from equation (35) as the product

w w w=Y Y F ,0¯ ( ) ¯ ( ) ( ) where w w=Y Ci0 ( ) ¯ is a passiveadmittance that does not undergo resonance and wF ( ) is aresonance-dependent function, i.e.

w w w

w w ep

wn

n

=

= =

=- + + -

- -

Y Y F

Y i C Ca

t

Fk J z k z J z

z J z J z

, ,

2 1 1

1. 36

T

j j j

j j j

0

0 33

2

p2

1 p2

0

0 1

¯ ( ) ¯ ( ) ( )

¯ ( ) ¯ ¯ ¯

( )( ¯ ) ( ¯ ) ( ¯ ) ¯ ( ¯ )

¯ ( ¯ ) ( ) ( ¯ )( )

Taking the real part of equation (36) yields the resonanceamplitude of the admittance real part, i.e.

= = -Y Y F Y F Y FRe Re Re Im Im . 37Re 0 0 0¯ ( ¯ ) ( ¯ ) ( ) ( ¯ ) ( ) ( )

Recall equations (4) and (7) and substitute intoequation (36) to get

w wep

we xp

w x ep

w x

= = = -

= + = +

Y Ca

t

a

ta

tC

i i i 1 i

i i , 38

T T

T

0 33

2

33

2

33

2

¯ ¯ ¯ ( )

( ) ( ) ( )

where C is the non-dissipative ideal capacitance, i.e.

ep

=

-

Ca

tnon dissipative ideal electrical capacitance . 39

T33

2

( ) ( )

Substitution of equation (38) into equation (37) yields

wx ww x

w w

= -= -= = ¼

Y C F C FC F F

j

Re ImRe Im

@ , 1, 2, 3, 40j

Re¯ ( ) ( )[ ( ) ( )]

( )

Equation (40) represents the amplitude of the resonancepeaks in the spectral plot of the admittance real part wY .Re¯ ( )To analyze the sensitivity with the modeling parameters ofequation (40), we write

d x dww x dw dx w x dw d

= -+ -+ +-

Y C F FF F C

C F C FC F

Re ImRe Im

Re ReIm . 41

Re¯ [ ( ) ( )][ ( ) ( )]

( ) [ ( )][ ( )] ( )

Note that dw is given in equation (30). Next, calculate dC,as shown below

dp

de ep

d ep

d

ep de

ee

p de

p d

= + -

= + -

Ca

t ta a

a

tt

a

t

a

t

a

a

a

t

t

t

2

2 . 42

T T T

TT

TT T

2

33 33 33

2

2

33

233

3333

2

33

2( )

Upon rearrangement, equation (42) becomes

ddee

d d= + -

⎛⎝⎜

⎞⎠⎟C C

a

a

t

t2 . 43

T

T33

33

( )

Since a and t are geometric dimensions, their thermalsensitivities are the corresponding coefficients of thermalexpansion, (a ,1 a ,3 ) and hence

d a d d a d= =a a T t t T, . 441 3 ( )

The temperature sensitivity of the dielectric permittivityeT

33 is not readily available; hence, we write

dee

d=¶¶T

T. 45TT

3333 ( )

Substitution of equations (44) and (45) into equation (43)yields

de

ed a d a d

ee

a a d

=¶¶

+ -

=¶¶

+ -

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

C CT

T T T

CT

T

12

12 . 46

T

T

T

T

33

331 3

33

331 3 ( )

The temperature sensitivity of the electrical dissipationfactor x is not readily available; hence, we write

dxxd=

¶¶T

T. 47( )

The temperature sensitivity of the resonance functionwF ( ) is too complicated to write explicitly; hence, we write

d d

d d

=¶

¶

=¶

¶

FF

TT

FF

TT

ReRe

ImIm

. 48

[ ( )] [ ( )]

[ ( )] [ ( )] ( )

The implicit assumption made in equations (46)–(48) isthat local linearization may be applied to obtain thetemperature sensitivity coefficients e¶ ¶T ,T

33 x¶ ¶T ,¶ ¶F TRe ,[ ( )] ¶ ¶F TIm .[ ( )] However, the reader iscautioned that linearization may be a localized phenomenonand may not be applicable over a large range of parametervariation.

9

Smart Mater. Struct. 25 (2016) 035024 V Giurgiutiu et al

Substitution of equations (30), (46)–(48) intoequation (41) yields

d x w

a a a

nn n

nd

w x

ee

a a d

wxd w x d

w d

= -

´ - + + -¶¶

+-

+¶¶

+ -

´¶¶

+ -

+¶¶

+¶

¶

-¶

¶

⎧⎨⎩⎡⎣⎢

⎤⎦⎥

⎫⎬⎭

⎛⎝⎜

⎞⎠⎟

Y C F F

s

s

T

z

z

TT

F F C

TT

C FT

T CF

TT

CF

TT

Re Im1

2

1

21

1 d

d

Re Im

12

ReRe

Im. 49

E

E

T

T

Re

1 2 311

11

2

33

331 3

¯ [ ( ) ( )]

( )[ ( ) ( )]

( ) [ ( )]

[ ( )] ( )

Upon rearrangement, we get

w

x

a a a

nn n

n

x

ee

a a

xx

¶¶

=

´

-

´ - + + -¶¶

+-

+¶¶

+ -

´¶¶

+ -

+¶¶

+¶

¶

-¶

¶

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎧⎨⎩⎡⎣⎢

⎤⎦⎥

⎫⎬⎭

⎛⎝⎜

⎞⎠⎟

⎤

⎦

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

Y

TC

F F

s

s

T

z

z

T

F F

T

FT

F

TF

T

1

2Re Im

1

21

1 d

d

Re Im

12

ReRe

Im

. 50

E

E

T

T

Re

1 2 311

11

2

33

331 3

¯

[ ( ) ( )]

( )[ ( ) ( )]

( ) [ ( )]

[ ( )]

( )

Equation (50) describes the temperature sensitivity of theadmittance peak amplitude real parts in terms of the modelingparameters sensitivities. A similar expression may be derivedfor the radiation sensitivity.

2.2.4. Sensitivity of the impedance peak amplitudes tomodeling parameters. The sensitivity of the impedancepeak amplitudes to modeling parameters can be examinedin the same way as the sensitivity of the admittance peakamplitudes and, in the end, an equation similar toequation (50) can be developed. For the sake of brevity,this development will not be included here.

2.2.5. Discussion of the sensitivity equations. Examination ofequations (32) and (33) reveals that the relative sensitivity of

the resonance and antiresonance frequencies with respect totemperature depends on the coefficients of thermal expansion,a ,1 a ,2 a ;3 on the compliance sensitivity w.r.t. temperature,¶ ¶s T;E

11 on the Poisson ratio sensitivity w.r.t. temperature,n¶ ¶T; and on the eigenvalue sensitivity w.r.t. Poisson

ratio nzd d .Examination of equation (50) reveals that the relative

sensitivity of the resonance amplitude of the admittance real-part spectrum with respect to temperature depends on thecoefficients of thermal expansion, a ,1 a ,2 a ;3 on thecompliance sensitivity w.r.t. temperature, ¶ ¶s T;E

11 on thePoisson ratio sensitivity w.r.t. temperature, n¶ ¶T; on theeigenvalue sensitivity w.r.t. Poisson ratio nzd d ; on thedielectric permittivity sensitivity w.r.t. temperature e¶ ¶T;T

33and the sensitivities of resonance function real and imaginaryparts, ¶ ¶F TRe ,[ ( )] ¶ ¶F TIm[ ( )] .

The above derivations did not explicitly deduce thesensitivities with respect to radiation exposure. This was notdone because the authors assume that similar relationsbetween the radiation and the material parameters exist asin the case of temperature sensitivities. Also, of course, theassumptions of local linearization of an implicitly nonlinearphenomenon also applies to radiation sensitivities as theyapply to temperature sensitivities.

However, most of these sensitivities are unknown atpresent; hence, it is hard to predict the overall sensitivity ofthe variables of interest including resonance and antireso-nance frequencies and spectral peak amplitudes. An extensivestudy is warranted, though not available at present, todetermine these sensitivities experimentally. Nonetheless,the experimental results presented in the second part of thisarticle will cast some light on the PWAS spectral andresonance behavior under temperature and radiation exposure.

2.3. Extension to the PWAS EMIS of a circular aluminum plate

When a PWAS transducer is applied to a structure, its EMISresponse changes drastically from the response of free PWASresonator. The E/M admittance and impedance curves willstill show resonance peaks, but these resonances will be thoseof the structure and not of the PWAS since the PWAS isconstrained by the structure and its oscillation follows thedynamic response of the structure. For the case of a circularPWAS transducer bonded to the center of a circular plate, [1]provides the following E/M admittance and impedance for-mulae

w w

nf n n c w

= -

´ -+

- - - +

⎡⎣⎢

⎤⎦⎥

⎫⎬⎭

Y C k

J z

J z J z

i 1

11

1 1,

51

p2

1

0 1

( ) ¯ { ¯

( ) ( ¯)¯ ( ¯) [( ) ( ) ¯ ( )] ( ¯)

( )

w ww

n ff f n n c w f

= = -

´ -+

- - - +

-

-⎡⎣⎢

⎤⎦⎥

⎫⎬⎭

Z YC

k

J

J J

1

i1

11

1 152

a

a a

1p2

1

0 1

1

( ) ( ) ¯ { ¯

( ) ( ¯ )¯ ( ¯ ) [( ) ( ) ¯ ( )] ( ¯ )

( )

10

Smart Mater. Struct. 25 (2016) 035024 V Giurgiutiu et al

The frequency dependent complex stiffness ratio c w¯ ( )that appears in equations (51) and (52) is given by

c ww

=k

k, 53str

PWAS¯ ( )

¯ ( )¯ ( )

where kPWAS¯ is the complex PWAS stiffness given by

n=

-k

t

as 1complex PWAS stiffness , 54

EPWAS11

¯¯ ( )

( ) ( )

The variable wkstr¯ ( ) is the dynamic structural stiffnessgiven by

å

å

wr

w z ww w

w z ww w

=- + +

+¢

- + +

=

=

-

⎜ ⎟

⎡⎣⎢⎢

⎛⎝

⎞⎠

⎤⎦⎥⎥

kha

r

U r

h W r

2 2i

2 2i. 55

a j N

Nj a

j j j

j N

Nj a

j j j

str

2 2

2 2

2 2

2 2

1

u u

uu

u u u

w w

ww

w w w

low

high

low

high

¯ ( )( )

( )( )

Note that the dynamic structural stiffness kstr¯ is a complexvariable. The variables Uju and Wjw are the modeshapes foraxial and flexural axisymmetric vibration of the circular plate.The summations forUju and Wjw in equation (55) go from Nu

low

to Nuhigh and from Nw

low to N ,whigh respectively, which are the

lower and higher axial and flexural mode numbers that bracketthe frequency range of interest. Detailed expression of the platemodeshapes and natural frequencies are given in [1] and willnot be repeated here for the sake of brevity. What is remarkableis that the resonances of the E/M admittance and impedancespectra of the PWAS transducer bonded to the structureoverlap almost exactly over the mechanical resonances of the

plate as depicted in the frequency response function. Thisoverlap is clearly indicated in figure 4. Hence, in the case of aPWAS bonded to a structure, the study of sensitivities shouldtake into account not only the sensitivity of the PWAS materialparameters but also the sensitivity of the structural parameterson which the PWAS transducer is attached and of whichresonance behavior the PWAS measures.

3. Experiments

Experiments were performed in order to subject the PWASspecimens to several environmental stress factors such as: (a)

Figure 4. Overlap of calculated frequency response function (FRF), E/M admittance ( YRe ) and E/M impedance ( ZRe ) showingcoincidence of peaks for a 0.8 mm thick, 100 mm diameter aluminum plate with a centrally placed circular PWAS transducer of= =d a2 6. 98 mm, =t 0.216 mm,a = ´s 18 10 Pa ,E

1112 1– – = ´ -d 175 10 m V ,31

12 1– – APC-850 piezoceramic, h x= = 1%.

Figure 5. PWAS-WL transducer showing feedback electrodes andsolder connections.

11

Smart Mater. Struct. 25 (2016) 035024 V Giurgiutiu et al

extreme hot and cold temperatures; (b) irradiation; and (c)advanced vacuum.

3.1. Experimental specimens

The experimental specimens considered in this study werecircular PWAS-WL (‘wire-lead’) transducers. This PWAStype has the bottom electrode wrapped around to the top suchthat the solder connection is only on the upper side of thePWAS (figure 5). Though convenient for installation, thearrangement of the electrodes imparts a certain asymmetrywhich may affect the vibration modes of the free PWAS. ThePWAS-WL transducers were purchased from the STEMINCCompany (http://www.steminc.com/), model numberSMD07T02S412WL. No data was available from the supplierabout the PWAS behavior under harsh environmental con-ditions as considered in our research.

3.2. Simulated space-environment conditions

3.2.1. Extreme temperature exposure. The extremetemperature exposure (figure 6) was obtained with a BinderFD-115 convention oven that has a digital temperaturecontroller for heating up to +300 °C, as well as a cryogenicdewar vessel for submersion in liquid nitrogen at –196 °C.

3.2.2. Vacuum exposure. The outer space vacuum can reach-10 Pa.14 The high vacuum conditions would affect products

with materials containing volatile compounds. Vacuumpressures lower than -10 Pa1 were achieved by using tritiummanifold, a high vacuum installation (figure 7), containing aTSH-171E Pfeiffer high vacuum pump with -10 Pa11 pressurelimit and TPG 262 Pfeiffer pressure vacuum controllers.

3.2.3. Radiation exposure. The cosmic radiation wassimulated with γ-radiation fields emitted by 60-Coradioactive sources. The experiments were conducted in agamma irradiation chamber 5000 (BRIT India http://www.

britatom.gov.in/index.html) (figure 8(a)), which is a compactself-shielded cobalt-60 gamma irradiator providing anirradiation volume of approximately 5000 c.c.. The materialfor irradiation is placed in an irradiation chamber located inthe vertical drawer inside the lead flask. This drawer can bemoved up and down with the help of a system of motorizeddrivers which enables precise positioning of the irradiationchamber at the center of the radiation field that is provided bya set of stationary Co-60 sources placed in a cylindrical cage.The sources are doubly encapsulated in corrosion resistantstainless steel pencils. A mechanism for rotating/stirringsamples during irradiation is also incorporated. The leadshield provided around the source is adequate to keep theexternal radiation field well within permissible limits.

The desired irradiation doses were calculated using thefollowing literature data: (a) full dose estimated for a missionto Mars (for a period of minimum solar activity) is110 mGy yr−1 average, thus a dose rate of about 15 μGy h−1;and (b) the largest fully absorbed doses determined byPioneer 10 and 11 space probes during the entire flight andthe crossing of high risk areas were 15 and 4.3 kGy,respectively. Therefore, the dose rate determined by Gammairradiation Chamber 5000 was considered to be representa-tive. The absorbed dose was set at full 23.5 kGy, whichcorresponds to 5 h of exposure at the measured dose rate of4.7 kGy h−1.

Given special test conditions (the size of the Gammachamber 5000, the need for vacuum pressurization andthermal insulation, etc), an irradiation enclosure (figure 8(a))was designed and built to accommodate the dewar vessel withPWAS specimens (figure 8(b)).

3.3. EMIS measurements

The EMIS was performed with an HP 4194A impedanceanalyzer (figure 6(e)) to measure the EMIS signatures of thefree PWAS. When connected to a free PWAS, the EMISequipment applies a continuous sinusoidal electrical signal of

Figure 6. Extreme temperature exposure equipment: (a) binder FD-115 convention oven with digital temperature controller for heating up to300 °C and HP 4194A impedance analyzer used for EMIS measurements; and (b) dewar vessel for cryogenic cooling at liquid nitrogentemperature.

12

Smart Mater. Struct. 25 (2016) 035024 V Giurgiutiu et al

fixed frequency and measures the amplitude ratio between thevoltage and the current as well as the phase shift, thusobtaining the complex impedance at a given frequency. Theimpedance analyzer can give the real and imaginary parts ofthe impedance, or alternatively, the magnitude and phase. By

sweeping a preset range of frequencies, one obtains the EMISsignature of the analyzed specimen. During the EMIS tests,the free PWAS specimens were placed in a free hangingposition such as to vibrate freely and avoid unwantedboundary condition effects.

Figure 7.Vacuum exposure equipment: tritium manifold high vacuum installation with high vacuum pump TSH-171E Pfeiffer with TPG 262Pfeiffer pressure controllers.

Figure 8. Radiation exposure combined with vacuum and cryogenic conditions: (a) irradiation enclosure of the gamma irradiation chamber5000 connected to the tritium manifold high vacuum installation; and (b) specimens in cryogenic dewar vessel.

13

Smart Mater. Struct. 25 (2016) 035024 V Giurgiutiu et al

4. Experimental results

Initial experiments were conducted to explore if the PWAStransducers would be affected by harsh RTV conditions thatare foreseen in the space-environment. Further experimentswere conducted to determine the temperature sensitivities ofthe PWAS resonance and antiresonance frequencies.

4.1. RTV exposure results

Nine PWAS transducers (#200 through 209) were subjectedto RTV exposure experiments. The first objective of theseexperiments was to determine if the PWAS transducers cansurvive the RTV exposure. If the PWAS can survive the RTV

exposure, then these experiments would also pursue a secondobjective. The second objective of these experiments was thatis to evaluate the changes that the RTV exposure introducedin the EMIS signature. Hence, EMIS signatures were takenbefore and after the exposure and the EMIS spectra wereexamined to identify changes in their characteristics.

Table 2 presents an overview of these RTV experiments.As indicated in table 2, five exposures were performed (testcycles no. 1 through no. 5). All test cycles except no. 4consisted of three steps:

(1) ½ h irradiation simultaneous with cryogenic temper-ature (–196 °C) and high vacuum. The cryogenictemperature was obtained through immersion in liquidnitrogen.

Table 2. Overview of the radiation, temperature, vacuum (RTV) experiments.

14

Smart Mater. Struct. 25 (2016) 035024 V Giurgiutiu et al

(2) 1 h irradiation at room temperature and pressureconditions.

(3) ½ h irradiation simultaneous with elevated temperature(+100 °C) and high vacuum.

Test cycle no. 4 was different; it consisted of 1 h irra-diation simultaneous with high vacuum at room temperature.

As indicated in table 2, EMIS measurements were takeninitially (RTV-0) and after each test cycle (RTV-1 throughRTV-5). The EMIS frequency range was 200–400 kHz whichencompasses the first resonance and antiresonance fre-quencies of the free PWAS which were approx. 305 and345 kHz, respectively.

The measured EMIS signatures were plotted and inter-preted. Here, we discuss the results for PWAS-200. Theresults for the other PWAS samples were similar.

The admittance and impedance plots for PWAS-200 arepresented in figures 9 and 10 with both full-range and narrow-band plots presented. The full-range plots are in the fullmeasured range of 200–400 kHz while the narrow-band plotsare centered around 305 kHz for admittance and around

345 kHz for impedance. As shown in figures 9(a) and 10(a),the full-range plots indicated that the general shape andposition of the resonance and antiresonance peaks are pre-served and that the effect of the RTV exposure is only slight.

A zoomed-in view of the resonance and antiresonancepeaks is presented in the narrow-band plots of figures 9(b)and 10(b), respectively. The actual values, frequencies, andamplitudes at the peaks are given in table 3. Plots of thesevalues are given in figure 11.

Examination of figure 11 indicates that no clear trend canbe established about the effect of RTV exposure on theseparameters. (Quadratic trend lines were tentatively drawn infigure 11, however they are only qualitative because the RTVeffects in these experiments were overlapped.)

Also given in table 3 are statistical measures of the meanand the standard deviation. Examination of table 3 indicatesthat the changes in resonance and antiresonance frequenciesare very small (0.25% and 0.49%, respectively), however, thechanges in resonance and antiresonance amplitudes are larger(16.4% and 13.7%, respectively).

Figure 9. Amittance plots showing the effect of RTV exposure on the resonance peaks for PWAS 200: (a) full-range plot; and (b) narrowband plot near the resonance frequency.

15

Smart Mater. Struct. 25 (2016) 035024 V Giurgiutiu et al

The conclusions of this set of experiments are:

• PWAS transducers can survive RTV exposure ofsimulated space-environment RTV conditions and canmaintain their functionality after several cycles of RTVexposure.

• The resonance and antiresonance frequencies of PWAStransducers are only slightly affected by exposure tosimulated space-environment RTV conditions. Typicalfrequency changes due to the presence of small cracks/flaws are of the order of 5%–10% ([1], page 878, table

Figure 10. Impedance plots showing the effect of RTV exposure on the antiresonance peaks for PWAS 200: (a) full-range plot; and (b)narrow band plot near the antiresonance frequency.

Table 3. Radiation, temperature, vacuum (RTV) exposure effects on resonance and antiresonance frequencies and peak amplitudes forPWAS 200.

f_Y, kHz ReY, mS f_Z, kHz ReZ, kOhm

Value % Change Value % Change Value % Change Value % Change

RTV-0 307.1 107.1 345.1 2.645RTV-1 307.6 0.16% 101.8 −4.9% 344.6 −0.14% 2.139 −19.1%RTV-2 308.1 0.16% 84.92 −16.6% 347.1 0.73% 2.129 −0.5%RTV-3 307.1 −0.32% 84.04 −1.0% 344.1 −0.86% 2.769 30.1%RTV-4 307.1 0.00% 80.76 −3.9% 343.1 −0.29% 3.008 8.6%RTV-5 305.6 −0.49% 63.64 −21.2% 341.6 −0.44% 2.976 −1.1%

Mean 307.1 87.0 344.3 2.6STD 0.76 14.26 1.70 0.36STD, % 0.25% 16.4% 0.49% 13.7%

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15.3 data). Hence, an SHM method based on trackingdamage-induced changes in the resonance and antireso-nance frequencies will not likely be affected by exposureto the harsh space-environment conditions.

• However, the use of an SHM method based on trackingthe peak amplitudes would not be recommended becausethese values are more strongly influenced by the harshspace-environment conditions.

After determining that the PWAS transducers can survivethe RTV exposure, we performed experiments to try todetermine the sensitivity of PWAS transducer to such harshenvironmental exposure as discussed in the next section.

4.2. Determination of temperature sensitivities

The next step in our investigation was an attempt to measurethe sensitivities defined by equations (33) and (50). In order todo this, we separated the RTV exposure in its fundamentalcomponents: (a) radiation, R; (b) temperature, T; and (c)vacuum, V. We then attempted to vary only one of theseenvironmental parameters and measure the effect of thisvariation on the resonance and antiresonance behavior of thePWAS transducers.

Of the three RTV environmental parameters, the temp-erature is the one that can be more readily varied in a con-trolled manner without too stringent safety requirements.

Hence, our sensitivity experiments were performed by vary-ing the temperature under atmospheric pressure and non-radiation conditions.

In the temperature sensitivity experiments, five PWAStransducers (# 321 through 325) were subjected to increasedtemperature using a Binder FD 115 controlled temperatureoven. The EMIS measurements were taken after the temper-ature reached steady state at the following values: 25 °C,50 °C, 75 °C, 100 °C, 125 °C, 150 °C, 175 °C, 200 °C. Themeasured EMIS data for PWAS 321 is given in figure 12(admittance) and figure 13 (impedance) where both full-rangeand narrow band plots are presented. The full-range plots arein the full measured range of 200–400 kHz while the narrow-band plots are centered around 310 kHz for admittance andaround 340 kHz for impedance.

As shown in figures 12(a) and 13(a), the full-range plotsindicated that the general shape and position of the resonanceand antiresonance peaks are preserved. The effect of exposureto increasing temperature seems to be a shift in the resonanceand antiresonance frequencies and modification of thecorresponding peaks.

A zoomed-in view of the resonance and antiresonancepeaks is presented in the narrow-band plots of figures 12(b)and 13(b), respectively. The actual values, frequencies andamplitudes at the peak, are given in table 4. Plots of thesevalues are given in figure 14. (The data point at 100 °C was

Figure 11. RTV exposure effect on resonance (admittance ReY) and antiresonance (impedance ReZ) peaks for PWAS 200: (a) resonancefrequency; (b) amplitude at resonance; (c) antiresonance frequency; and (d) amplitude at antiresonance.

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excluded from these plots because it displayed outlierbehavior.)

Examination of figures 14(c) and (d) indicates a lineartrend. The linear trend was confirmed by a high R value(0.9647 for antiresonance frequency and 0.9357 for impe-dance amplitude at antiresonance). The linear tendency is forthe antiresonance frequency and ReZ amplitude to decrease astemperature increases. The coefficients of these linear trendswere used to calculate the physical sensitivities of the anti-resonance frequency and the antiresonance peak ReZ. Divi-sion of the physical sensitivities by the mean values of therespective quantities yielded the relative sensitivities.

Examination of figures 14(a) and (b) indicates a quadratictrend in the admittance behavior at the resonance frequency.The resonance frequency seems to decrease at first, afterwhich it starts to increase at an accelerating rate (figure 14(a)).The admittance amplitude ReY seems to increase at first andthen flattens out and starts to decrease (figure 14(b)).

Also given in table 4 are statistical measures of the meanand the standard deviation. Examination of table 4 indicatesthat the changes in resonance and antiresonance frequenciesare rather small, 1.01% and 0.35%, respectively. However,the changes in resonance and antiresonance amplitudes arelarger, 23.2% and 18.2%, respectively.

The conclusions of this set of experiments are:

• The antiresonance frequency and amplitude ReZ seem tohave a linear dependence on temperature showing agradual decrease of their values as temperature increases

• The resonance frequency and amplitude ReY seem tohave a more complicated behavior. The resonancefrequency shows an increase with temperature, whereasthe amplitude ReY increases and then flattens out.

• The physical temperature sensitivity of the antiresonancefrequency for PWAS 321 is approximately 21.5 Hz °C.The relative temperature sensitivity of the antiresonancefrequency is approximately ´ -63.1 10 C6 .

• The physical temperature sensitivity of the antiresonanceamplitude ReZ for PWAS 321 is approximately 4.7Ω/°C.The relative temperature sensitivity of the antiresonanceamplitude ReZ is approximately ´ -3.31 10 C3 .

4.3. Tentative statistical analysis

A tentative statistical analysis of the measured results wasalso conducted. In the RTV category, we studied compara-tively the results for six PWAS resonators, i.e., PWAS 200,PWAS 203, PWAS 204, PWAS 207, PWAS 212, PWAS227. The results of these comparative studies are given intable 5 through table 8. On the one hand, examination oftable 5 reveals that the average standard deviation of

Figure 12. Amittance plots showing the effect of temperature on the resonance peaks for PWAS 321: (a) full-range plot; and (b) narrow bandplot near the resonance frequency.

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resonance frequency among the six PWAS resonators and thesix RTV exposure cases is only 0.27%. Similarly, examina-tion of table 7 reveals that the average standard deviation ofthe antiresonance frequency is 0.42%. These small values,which are less than 0.5%, indicate that the resonance andantiresonance frequencies are affected very little by RTVexposure during the reported tests. This statistics-based con-clusion is consistent with the conclusion presented for a single

PWAS resonator in section 4.1. On the other hand, exam-ination of table 6 reveals that the average standard deviationof resonance amplitudes among the six PWAS resonators andthe six RTV exposure cases is 14.9%, whereas table 8 indi-cates that average standard deviation of the antiresonanceamplitudes is 12.3%. This indicates that the resonance andantiresonance amplitudes are more greatly affected muchmore by RTV exposure. This statistics-based conclusion is

Figure 13. Impedance plots showing the effect of temperature on the antiresonance peaks for PWAS 321: (a) full-range plot; and (b) narrowband plot near the antiresonance frequency.

Table 4. Temperature effects on resonance and antiresonance frequencies and peak amplitudes for PWAS 321.

f_Y, kHz ReY, mS f_Z, kHz ReZ, kOhm

T, °C Value % Change Value % Change Value % Change Value % Change

25 305.0 50.2 343.3 1.72350 303.3 −0.56% 59.9 19.2% 342.1 −0.35% 1.820 5.6%75 304.3 0.33% 80.9 35.1% 342.0 −0.03% 1.655 −9.1%100 303.8 −0.16% 92.8 14.8% 340.2 −0.53% 1.605 −3.0%125 306.1 0.76% 103.9 12.0% 340.5 0.09% 1.398 −12.9%150 310.3 1.37% 67.7 −34.9% 340.1 −0.12% 1.266 −9.4%175 311.8 0.48% 93.9 38.8% 340.0 −0.03% 1.022 −19.3%200 316.8 1.60% 84.2 −10.3% 339.3 −0.21% 1.049 2.6%

Mean 308.2 77.2 341.0 1.419STD 3.15 18.78 1.22 0.28STD, % 1.02% 24.3% 0.36% 19.7%

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also consistent with the conclusion presented for a singlePWAS resonator in section 4.1.

A similar statistical analysis was also applied to thetemperature-only experiments performed on five PWASresonators, i.e., PWAS 321, PWAS 322, PWAS 323, PWAS324, PWAS 325. The results of these comparative studies aregiven in table 9 through table 12. On the one hand, exam-ination of table 9 reveals that the average standard deviationof resonance frequency among the five PWAS resonators andthe eight temperature exposure levels is only 1.05%.

Similarly, examination of table 11 reveals that the averagestandard deviation of the antiresonance frequency is 0.47%.These two values, which are around 1% or less, indicate thatthe resonance and antiresonance frequencies are only slightlyaffected by temperature exposure during the reported tests.This statistics-based conclusion is consistent with the con-clusion presented for a single PWAS resonator in section 4.2.On the other hand, examination of table 10 reveals that theaverage standard deviation of resonance amplitudes amongthe five PWAS resonators and the eight temperature exposure

Figure 14. Temperature effect on resonance (admittance ReY) and antiresonance (impedance ReZ) peaks for PWAS 321: (a) resonancefrequency; (b) amplitude at resonance; (c) antiresonance frequency; and (d) amplitude at antiresonance. The continuous curves are tentativelinear trend lines.

Table 5. Comparative radiation, temperature, vacuum (RTV) exposure effects on resonance frequency, f_Y, for six PWAS resonators.

f_Y, kHz

PWAS 200 PWAS 203 PWAS 204 PWAS 207 PWAS 212 PWAS 227

RTV-0 307.1 296.1 302.1 302.1 304.1 290.1RTV-1 307.6 295.6 302.6 302.6 304.1 290.1RTV-2 308.1 296.1 302.1 302.1 304.1 289.6RTV-3 307.1 296.6 301.6 301.6 304.1 289.6RTV-4 307.1 295.6 301.1 301.1 302.1 291.6RTV-5 305.6 297.1 303.1 303.1 304.6 293.6

Mean 307.1 296.2 302.1 302.1 303.9 290.8STD 0.764 0.534 0.645 0.645 0.804 1.434 Average STD %STD, % 0.25% 0.18% 0.21% 0.21% 0.26% 0.49% 0.27%

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levels is 25.3%, whereas table 12 indicates that averagestandard deviation of the antiresonance amplitudes is 21.6%.This indicates that the resonance and antiresonance ampli-tudes are more strongly affected by the temperature exposure.This statistics-based conclusion is also consistent with theconclusion presented for a single PWAS resonator insection 4.2.

An overlap of all the RTV data is given in figure 15whereas an overlap of the temperature-only data is given infigure 16. It is apparent that some common trends may exist,

but they are not immediately quantifiable. A completeANOVA analysis of the data would be required for a com-plete statistical analysis, but this is beyond the scope of thisarticle and will not be attempted here.

5. Summary and conclusions

This study has discussed the effect of RTV on PWAS. Themotivation for this study is the intention to extend SHMmethods to space vehicle applications. The harsh space

Table 6. Comparative radiation, temperature, vacuum (RTV) exposure effects on resonance amplitude (ReY) for six PWAS resonators.

ReY, mS

PWAS 200 PWAS 203 PWAS 204 PWAS 207 PWAS 212 PWAS 227

RTV-0 107.1 42.8 71.6 77.0 75.9 53.8RTV-1 101.8 32.2 54.6 70.4 62.1 48.9RTV-2 84.9 41.4 62.8 64.5 55.4 41.3RTV-3 84.0 43.1 61.0 60.1 55.7 36.7RTV-4 80.8 37.7 58.2 57.9 32.8 36.4RTV-5 63.6 34.9 58.6 47.9 74.0 46.2

Mean 87.0 38.7 61.1 62.9 59.3 43.9STD 14.26 4.109 5.329 9.28 14.32 6.366 Average STD %STD, % 16.4% 10.6% 8.7% 14.7% 24.1% 14.5% 14.9%

Table 7. Comparative radiation, temperature, vacuum (RTV) exposure effects on antiresonance frequency, f_Z, for six PWAS resonators.

f_Z, kHz

PWAS 200 PWAS 203 PWAS 204 PWAS 207 PWAS 212 PWAS 227

RTV-0 345.1 333.6 337.1 340.6 342.6 330.6RTV-1 344.6 333.1 342.6 340.6 343.1 331.1RTV-2 347.1 332.6 337.1 338.1 342.1 330.6RTV-3 344.1 332.6 336.6 340.1 341.6 330.1RTV-4 343.1 331.1 343.1 336.1 340.1 329.1RTV-5 341.6 333.1 337.1 341.1 342.6 330.6

Mean 344.3 332.7 338.9 339.4 342.0 330.4STD 1.7 0.786 2.779 1.772 0.975 0.629 Average STD %STD, % 0.49% 0.24% 0.82% 0.52% 0.29% 0.19% 0.42%

Table 8. Comparative radiation, temperature, vacuum (RTV) exposure effects on antiresonance amplitude (ReZ) for six PWAS resonators.

ReZ, kOhm

PWAS 200 PWAS 203 PWAS 204 PWAS 207 PWAS 212 PWAS 227

RTV-0 2.65 2.37 2.27 2.36 4.16 1.65RTV-1 2.14 2.99 2.02 3.05 3.32 1.57RTV-2 2.13 2.00 2.57 2.38 3.96 1.85RTV-3 2.77 1.40 2.61 2.36 4.18 1.92RTV-4 3.01 1.82 2.16 2.21 3.54 1.74RTV-5 2.98 2.31 2.22 2.37 4.03 1.53

Mean 2.61 2.15 2.31 2.46 3.87 1.71STD 0.359 0.493 0.212 0.271 0.324 0.141 Average STD %STD, % 13.7% 23.0% 9.2% 11.0% 8.4% 8.2% 12.3%

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environment conditions encompass extreme temperatures (hotand cold), cosmic radiation, and interplanetary vacuum. Theinvestigative method used in this study was the EMIS and thepresent study contains both theoretical and experimentalinvestigations.

5.1. Summary

The theoretical part of this study treated the modeling ofcircular PWAS transducers. Two boundary conditions wereconsidered: (a) free PWAS transducers acting as resonators;

Table 9. Comparative temperature effects on resonance frequency, f_Y, for five PWAS resonators.

f_Y, kHz

T, °C PWAS 321 PWAS 322 PWAS 323 PWAS 324 PWAS 325

25 305.0 300.9 306.2 298.4 301.750 303.3 298.4 304.3 295.9 300.475 304.3 297.7 303.6 295.1 299.5100 303.8 298.5 304.4 295.2 301.1125 306.1 298.7 305.7 295.2 301.2150 310.3 301 309 296.8 302.8175 311.8 303.7 311 298.2 305.5200 316.8 305.4 313.5 303.7 308.3

Mean 307.7 300.5 307.2 297.3 302.6STD 4.50 2.60 3.35 2.71 2.75 Average STD %STD, % 1.46% 0.87% 1.09% 0.91% 0.91% 1.05%

Table 10. Comparative temperature effects on resonance amplitude (ReY) for five PWAS resonators.

ReY, mS

T, d°C PWAS 321 PWAS 322 PWAS 323 PWAS 324 PWAS 325

25 50.2 47.6 58.9 34.3 49.150 59.9 51.8 64.3 36.0 44.275 80.9 53.9 68.0 35.8 48.2100 92.8 67.9 79.6 60.6 44.4125 103.9 63.8 66.6 64.9 65.2150 67.7 53.4 104.9 71.0 62.9175 93.9 63.2 139.5 83.4 33.9200 84.2 70.7 157.3 66.9 70.1

Mean 79.2 59.0 92.4 56.6 52.2STD 17.27 7.88 35.23 17.56 11.68 Average STD %STD, % 21.8% 13.4% 38.1% 31.0% 22.4% 25.3%

Table 11. Comparative temperature effects on antiresonance fr`uency, f_Z, for five PWAS resonators.

f_Z, kHz

T, ° C PWAS 321 PWAS 322 PWAS 323 PWAS 324 PWAS 325

25 343.3 338.1 348.9 341.0 340.050 342.1 335.9 346.8 339.1 339.275 342.0 335.0 345.2 337.5 338.0100 340.2 334.4 344.3 336.8 338.0125 340.5 333.2 343.6 336.2 337.5150 340.1 332.8 343.1 336.3 338.2175 340.0 332.4 342.5 336.2 339.0200 339.3 331.3 342.0 335.4 339.1

Mean 341 334 345 337 339STD 1.278 2.042 2.185 1.741 0.776 Average STD %STD, % 0.37% 0.61% 0.63% 0.52% 0.23% 0.47%

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and (b) PWAS transducers attached to structure and acting ashigh-frequency modal sensors of the local vibration in theirstructural neighborhood. The theoretical model of a PWASresonator was used to predict the resonance and antiresonancebehavior. The resonance condition was identified by a peak inthe admittance real part spectrum (ReY) whereas the

antiresonance condition was identified by a peak in theimpedance real part spectrum (ReZ). Closed-form analyticalsolutions were used for admittance wY ( ) and impedance aswell as to determine the admittance and impedance of aPWAS transducer mounted in the center of a circular discaluminum structure.

Figure 15. Overlapped RTV exposure effects on resonance (admittance ReY) and antiresonance (impedance ReZ) peaks for six PWAStransducers (PWAS 200, 203, 204, 207, 212, 227): (a) resonance frequency; (b) amplitude at resonance; (c) antiresonance frequency; and (d)amplitude at antiresonance.

Table 12. Comparative temperature effects on antiresonance amplitude (ReZ) for five PWAS resonators.

ReZ, kOhm

T, °C PWAS 321 PWAS 322 PWAS 323 PWAS 324 PWAS 325

25 1.723 2.717 1.579 2.945 3.16050 1.820 1.849 1.807 2.627 2.54575 1.655 1.919 1.665 2.631 2.290100 1.605 2.200 1.571 2.750 2.385125 1.398 2.009 1.386 2.338 2.050150 1.266 1.836 1.233 1.950 1.856175 1.022 1.648 1.067 1.555 1.758200 1.049 1.307 0.931 1.110 1.658

Mean 1.44 1.94 1.40 2.24 2.21STD 0.287 0.384 0.286 0.602 0.463 Average STD %STD, % 19.9% 19.9% 20.4% 26.9% 20.9% 21.6%

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The theoretical study continued with the derivation of thesensitivities. First, the sensitivity of the resonance frequencyto modeling parameters was discussed. A closed form solu-tion was derived to describe the relative temperature sensi-tivity of the resonance frequency, ¶ ¶f T f ,( ) with respect tothe coefficients of thermal expansion, a a a, , ;1 2 3 the Pois-son ratio, n, and its sensitivity, n¶ ¶T; the relative com-pliance gradient, ¶ ¶s T s ;E E

11 11( ) and the Bessel function root,z, and its sensitivity, ¶ ¶z T . The relative temperature sensi-tivity of the antiresonance frequency ¶ ¶f T fAR AR( ) wassimilarly derived. The temperature sensitivity of the admit-tance and impedance peaks was also considered.

The experimental part of this study examined behavior ofPWAS transducers when subjected to RTV that simulates theconditions that might be encountered on a space vehicle. Twosets of experiments are described; the first set of experimentsexamined if the PWAS transducers would be affected byharsh RTV conditions met in the space environment while thesecond set of experiments attempted to determine the temp-erature sensitivities of the PWAS resonance and anti-resonance frequencies.

In the first set of experiments, PWAS transducers weresubjected to several cycles of RTV conditions inside anirradiation chamber. Both elevated temperatures (+100 °C)and cryogenic temperatures (−196 °C) were applied. Themaximum cumulative absorbed radiation dose was 23.5 kGy.EMIS measurements were taken before and after each RTVcycle. Examination of these EMIS measurements revealedthat the PWAS transducers survived well even with repeatedRTV exposures and remained functional throughout. Exam-ination of EMIS data indicated that the resonance and anti-resonance frequencies changed by less than 1% due to RTVexposure whereas the resonance and antiresonance ampli-tudes changed by around 15%.

In the second set of experiments, PWAS transducers weresubjected to eight increasing temperatures in the 25 °C–200 °Crange. EMIS measurements were taken at each temperatureafter stabilization. Processing of the EMIS data determined thatthe relative temperature sensitivity of the antiresonance fre-quency f fAR AR is approximately ´ -63.1 10 C6 and therelative temperature sensitivity of the antiresonance amplitudeReZ is approximately ´ -3.31 10 C3 .

Figure 16. Overlapped temperature effects on resonance (admittance ReY) and antiresonance (impedance ReZ) peaks for five PWAStransducers (PWAS 321, 322, 323, 324, 325): (a) resonance frequency; (b) amplitude at resonance; (c) antiresonance frequency; and (d)amplitude at antiresonance.

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5.2. Conclusions and future work

This study has developed, for the first time, an analyticalderivation of the sensitivity of PWAS EMIS spectra toenvironmental changes and has deduced closed form solu-tions for the temperature sensitivity of spectral features suchas resonance and antiresonance frequencies and peaks. Thishas also, for the first time, examined the combined effect ofthe outer-space environment (radiation, extreme temperatures,and vacuum) on the resonance and antiresonance behavior ofcircular PWAS resonators.

It was found that the PWAS transducers survived wellthe exposure to simulated outer-space exposure and that thechanges in their resonance and antiresonance frequencies arequite small. Hence, SHM methods based on tracking damage-induced changes in the resonance and antiresonance fre-quencies will not likely be affected by the PWAS SHMequipment exposure to the harsh outer-space environment.However, the SHM methods based on tracking the peakamplitudes would not be recommended because these valuesare more strongly influenced by the harsh outer-spaceenvironment. These trends were statistically confirmed bycomparatively examining a batch of six PWAS resonatorsexposed to RTV conditions and a batch of five PWAS reso-nators exposed to temperature-only conditions. However, acomplete ANOVA statistical analysis was not attempted sinceit would be beyond the scope of this article.

It is important to note that this study is only pre-liminary. More sustained work is required to derive statis-tically significant data by testing a larger number of PWAStransducers and repeating some of the exposure tests in atrue design-of-experiments approach. In addition, the sensi-tivities measured in this study are insufficient for a fullunderstanding of the physics of the problem. Examination ofthe sensitivity formulae derived in this study reveals thatmuch is still unknown about the individual sensitivities ofthe constitutive parameters: Poisson ratio sensitivity, n¶ ¶T ,relative compliance gradient ¶ ¶s T s ,E E

11 11( ) and sensitivityof the Bessel function root ¶ ¶z T . Such topics should beaddressed in future work.

Acknowledgments

Partial support from the Romanian Space Agency throughSTAR project ID 188 is thankfully acknowledged.

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