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VIBRATION AND SHOCK ANALYSIS OF A MAST STRUCTURE

AGAINST MIL STD REQUIREMENTS

Lt Cdr JJ Mattam (DDND, IHQ MOD(N)DND SSG, New Delhi)

This paper is based on a structural analysis undertaken to validate the integrity of a mast structure against

dynamic loads due to vibration and shock. The vibration loads are considered as specified in MIL STD 167 and shock

load is considered for an underwater explosion. The shock load considered is the same as that considered for machinery

foundations sited on the keel of a ship. Though it is safe to assume that the shock load due to underwater explosion for

a mast structure will be much lesser than the load experienced by a machinery foundation, the worst case is considered

since no data regarding the damping of the shock load by the ship’s hull is available for the structure under consideration.

Key words: - Vibration; MIL STD; Mast; Shock; Underwater Explosion;

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INTRODUCTION

Overview

A ship structure and environment in

which it is operating constitute probably the

most formidable and complex of all structural

engineering problems in both the

determination of loading and response of the

structure. The ship structure is subjected to a

number of static and dynamic loads during its

service. The static loads include accelerations

due to ship motions, equipment weight, ballast

weight, fuel weight, wind loads, wave loads,

snow loads and, thermal loads. The dynamic

loads include wave loads, vibrations due to

ship’s main machinery, shafting and,

propeller, ballistic loads and, shock loads.

It becomes necessary to analyse a ship

structure for its response against various loads

to assess the structural integrity. A structure is

subjected to static and dynamic analyses to

substantiate the structural strength against

various loads. The MIL STD specifies criteria

for acceptance of a system or equipment to be

used in a military environment. The

foundations and structures on which the

equipment is being installed also need to be

tested against the MIL STD to confirm the

acceptable performance of the equipment /

system.

The structural analysis for

substantiating a structure against the MIL

STD criteria is explained in this paper. A mast

structure for installation of radar antenna is

considered. Modal analysis has been carried

out to assess natural frequencies of the

structure. It is further analysed to study the

structural response against vibration and

shock loads. The criteria for analyses are

derived based on the requirements explained

in different MIL STDs.

Vibration Loads

The ship structure experiences

vibrations from various sources such as main

machinery, shaft, propeller and, the hull

vibrations induced due to sea environment.

Misalignment of shafts and propeller

imbalance can cause forces at a frequency

equal to the shaft revolutions. A propeller

operating in a non-uniform flow is subject to

forces at blade rate frequency, which is equal

to shaft rpm multiplied by number of blades of

the propeller. In addition, a propulsor induces

pressure variations in the surrounding water

and on ship’s hull in the vicinity. A ship hull

may also experience hull vibrations due to

absorption of wave energy. The rotating

machinery onboard the ship such as turbines,

electric motors, and, other reciprocating

machinery can also induce vibrations on the

ship structure.

Even though vibration loads may seem

unassuming, they can be fatal if the vibration

frequencies match with natural frequency of

structure. Vibration loads can give rise to

response prominence due to resonance when

frequency of vibration is of the order of

natural frequency of structure. Since local

vibration response of a ship structure to a

disturbing force is curable by way of changing

natural frequency of structure, it is important

to carry out the vibration analysis to assess the

presence of any response prominence.

The MIL STD 167 (Department of

Defence, 2005) is applicable to shipboard

equipment subjected to mechanical vibrations

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from the environmental and internal excitation

caused by unbalanced rotating components of

naval shipboard equipment. This standard

divides the vibrations into two categories;

Type I Environmental Vibrations and, Type II

Internally Excited Vibrations. Environmental

vibration is vibratory force, which is imposed

on equipment installed aboard ships, caused

by the hydrodynamic forces on the propeller

blades interacting with hull and by other

sources. Internally excited vibration is

vibration of machinery generated by mass

unbalance of a rotor.

As per MIL STD 167, equipment

intended for installation solely on a particular

ship class need only be vibrated from 4 Hz to

(1.15 x maximum design rpm x number of

propeller blades/60) rounded up to the nearest

integer frequency or the maximum test

frequency as specified for substantiating the

equipment against Environmental Vibrations.

Internally excited vibration requirements shall

apply to the procurement of rotating

machinery only.

Shock Loads

A structure or equipment in a military

environment can experience shock from

various sources such as explosions, collisions

etc. An underwater explosion is likely to cause

maximum damage to a warship. It is a

phenomenon which is studied by ship

designers and anti-ship weapon designers

alike. The pulsating bubbles due to the

underwater explosion create pressure waves

with frequency close to the fundamental hull

modes of vibration of small ships. The effect

of underwater explosion becomes severe

when it causes the ship to whip. It also creates

shock waves which carry about one third of

the energy of explosion. These waves are

transmitted through water, into and through

the ship’s hull causing shock and possible hull

rupture. The effects due to an underwater

explosion are depicted in Figure 1 (K J

Rawson, 2001).

Figure 1: Effects of an Underwater Explosion

In order to undertake an underwater

explosion analysis, amount of data required

and computational power required are

phenomenal. Such an analysis may be

required to assess the integrity of entire hull of

a ship. However, for a structure like an

antenna mast, entire effects of underwater

explosion may not be required to be

considered. The most important factor to be

considered for such a structure is the shock

loading due to underwater explosion. Intensity

of shock experienced by the hull of the ship

will depend on the distance, orientation and

size of the explosion relative to ship. The

effect of shock will further reduce in case of a

mast structure since a large amount of shock

energy will be absorbed by ship’s hull itself.

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MIL STD 901 (Department of

Defence, 1989) defines the weight and type of

explosive and distance of explosion from the

platform against which an equipment or

system is to be tested. A lot of studies have

been carried out to assess the effect of

underwater explosions on floating bodies.

These studies have successfully assessed the

amplitude and frequency of shock waves as

well as the peak pressure of shock wave front.

The studies have shown that the average

amplitude of the surface shock waves is of the

order of 15g and the half time period of such

shock waves is of the order of 10-12

milliseconds corresponding to an underwater

explosion caused by the amount of explosive

as specified in the MIL STD.

Finite Element Model

The mast structure was modeled using

AutoCAD 3D and the model was exported to

FE software. The mast is considered to be

made of structural steel for all practical

purposes. The physical properties of structural

steel are tabulated in Table 1.

Table 1: Properties of Structural Steel

Property Value

Yield Stress of Steel 250 MPa

Ultimate tensile

strength

4.6 e+08 Pa

Young’s modulus

of steel

2.1 e+11 Pa

Poisson’s ratio 0.3

Density of Steel 7850 kg/m3

Bulk Modulus 1.6 e+11 Pa

Shear Modulus 7.6 e+10 Pa

The meshing of the model was carried

out in such a manner to optimize the mesh

taking into consideration computational

facilities available and completion time for

analysis. The mesh contains elements with

sizes varying from 0.45m to 0.005m. Model is

considered to be fixed at the bottom for

analysis. The finite element model is shown in

Fig 2.

Figure 2: FE Model of Mast

Vibration Analysis

Modal analysis of the structure is a

pre-requisite to carry out any kind of vibration

analysis of the structure. The modal analysis

gives natural frequencies of the structure.

After determining the natural frequencies,

harmonic vibration analysis of the structure is

carried out since the vibrations required to be

considered as per MIL STD are discreet

frequencies. The vibration analysis has been

carried out only for the environmental

vibrations since the internal excitation is

required only in the case of rotating

machinery.

The minimum frequency required to

be considered for the harmonic vibration

analysis as per MIL STD is 4 Hz. The

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maximum frequency required as per MIL STD

167 criteria based on the design rpm of the

propeller of the ship under consideration is 14

Hz. However, as a standard practice 1.5 times

the highest frequency is considered for

harmonic vibration analysis. Therefore the

harmonic vibration analysis of the structure

has been carried out for frequencies from 4 to

21 Hz.

The amplitude of vibration to be

considered has been defined in MIL STD. The

same is depicted in Figure 3. In addition

pressure due to wind of 2532.85 Pa has also

been applied on the structure during the

vibration analysis.

Figure 3: Environmental Vibration Limits

The first natural frequency of the

structure was found to be 19.112 Hz from the

Modal Analysis. The vibration analysis was

carried out to assess the stress, deformation

and, acceleration on the antenna mounting

surface due to vibrations.

Shock Analysis

A transient analysis of the structure

has been carried out to assess its response to

shock load. The shock load is applied as base

excitation of 15g, 20ms sine wave. This sine

wave is depicted in Fig 4. This value is taken

based on the studies on underwater explosions

available in the open source. The open source

values are for surface shock waves. The shock

waves acting on a mast structure will have a

much lesser amplitude than the surface shock

wave. However, the amplitude of the shock

wave has been considered for the analysis

since no data is available on damping due to

the ship’s hull.

Figure 4: 15g, 20ms Shock Sine Wave

The sine wave is applied as a base

excitation. This can be considered as a safe

assumption since the mast and ship can be

considered as a spring-mass system under

forced vibration. The ship’s hull can be

considered as base and mast can be equated to

mass. The spring and damper depict structural

rigidity and damping provided by ship’s hull.

The ship’s hull will be undergoing whipping

motions due to an underwater explosion which

can be equated as base excitation. This spring-

mass system is depicted in Fig 5.

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Figure 5: Mass-Spring system with Base

Excitation

Results and Discussions

The natural frequency of the structure

has been assessed from Modal Analysis. The

first natural frequency of the structure is

19.112 Hz. The frequencies for first six modes

of vibrations are tabulated in Table 2. The plot

showing the first mode of vibration is shown

in Fig 6.

Table 2 : Natural Frequencies of Mast

Modes Natural

Frequency ( in Hertz)

1 19.112

2 22.776

3 26.647

4 31.251

5 37.096

6 44.746

Figure 6: First Natural Frequency of Mast

The vibration analysis of the structure

was carried out for frequencies from 4-21 Hz.

The stress, deformation and, acceleration of

the structure has been assessed for all the

frequencies in the range. The plots of stress,

deformation and, acceleration of the structure

at 19.545 Hz are shown in Fig 7-9. This is the

frequency at which the structure experiences

resonance.

Figure 7: Plot showing Stress at Resonance

Figure 8: Plot showing Acceleration at

Resonance

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Figure 9: Plot showing Deformation at

Resonance

The shock analysis of the structure

against a 15g, 20ms sine wave has been

carried out by applying it as a base excitation

in X, Y and, Z directions independently. The

analysis has been carried out using the

transient method. The stress and deformation

of the structure is found to be maximum when

the shock is applied in Y direction. The plots

of stress and deformation of structure for

shock load applied in Y direction are shown in

Fig 10 and 11.

Figure 10: Plot showing deformation due to

Shock Load

Figure 11: Plot showing Stress due to

Shock Load

The modal analysis has shown that the

first natural frequency of the structure is

19.112 which falls within the range of

frequencies considered for analysis. The

presence of resonance can be inferred from the

amplitude vs frequency plots for acceleration,

deformation and, stress shown in Fig 12-14.

The amplitudes suddenly increase as the

frequency of vibration approaches natural

frequency of structure. Even though the

amplitudes are higher at resonance frequency,

the values of deformation and stress are well

within the acceptable values. The maximum

deformation is ~8mm and maximum stress is

~65 MPa and these values are not occurring on

the bulkhead mounting the antenna. Further,

the resonating frequency is beyond the actual

range that need to be considered as per MIL

STD. Therefore it is concluded that the

structure meets the requirements as laid out in

MIL STD 167.

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Figure 12: Amplitude vs Frequency -

Acceleration

Figure 13: Amplitude vs Frequency -

Deformation

Figure 14: Amplitude vs Frequency - Stress

The shock analysis has shown that the

maximum stress acting on the structure due to

the shock loading is 28.28 MPa. The yield

strength of structural steel is 250 MPa.

Therefore it can be inferred that the structure

has a factor of safety of eight against a shock

load of amplitude 15g and time period 20ms.

Figure 15: Plot showing Factor of Safety

against Shock Load

REFERENCES

Department of Defence. (1989, Jul). MIL STD

901 D. Requirements for Shock Tests.

Department of Defence.

Department of Defence. (2005). MIL STD

167 1A. Mechanical Vibrations of Shipboard

Equipment. Department of Defence.

K J Rawson, E. C. (2001). Basic Ship Theory.

Oxford: Butterworth-Heinemann.

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Details of Authors

Name :- Lt Cdr JJ Mattam

Designation :- DDND

Company :- Indian Navy

Address :- IHQ MOD(N)/DND SSG

A-33, Kailash Colony

New Delhi – 110048

Phone :- 8129597385