Procedia Engineering 51 ( 2013 ) 703 – 708

1877-7058 © 2013 The Authors. Published by Elsevier Ltd. Open access under CC BY-NC-ND license.

Selection and peer-review under responsibility of Institute of Technology, Nirma University, Ahmedabad.doi: 10.1016/j.proeng.2013.01.100

on Engineering (NUiCONE 2012)

Finite Element Analysis of Double Cracked Beam and its Experimental Validation

Irshad A Khan*, Dayal R Parhi Department of Mechanical Engineering, National Institute of Technology, Rourkela 769008, India

Abstract

The objective of this paper is to estimate the effects of crack depth on natural frequency and mode shape of beam; Cantilever and fixed-fixed beam are engaged for analysis. The presence of cracks a severe threat to the performance of structures and it affects the vibration signatures (Natural frequencies and mode shapes).Here two transverse cracks are deemed on the beam at 200 mm and 600mm from fixed end of the beam, the depth of cracks are varied from 0.5mm to 3mm at the interval of 0.5mm. Modeling and Numerical simulation is established using commercially available finite element analysis software package ANSYS. Based on convergence study a higher order 3-D, 10-node element having three degrees of freedom at each node, SOLID 187 element is used in analysis. Natural frequency increases and Mode shape decreases as the crack depth increases. Experiment are also conducted, results of experiment having good co-relation with results of finite element analysis. © 2012 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Institute of Technology Nirma University,Ahmedabad.

Keywords: Natural frequency, Mode shape,Crack, Ansys,

1. Introduction

Health monitoring and the analysis of damage in the form of crack in Beam like structures are important not only for leading safe operation but also retraining system performance. Since long efforts are on their way to find a realistic solution for crack detection in beam structures in this regard many approaches have so far being taken place. When a structure suffers from damages, its dynamic properties can change. Crack damage leads to reduction in stiffness also with an inherent reduction in natural frequency and increase in modal damping. The paper lends a viable relationship between the modal natural frequency and mode shape at the different crack depth. Since last few decade free vibration analysis has become a topic of many studies therefore attention is focused on it only. Damage identification on a composite cantilever beam through vibration analysis using finite element analysis software package ANSYS is established by Ramanamurthy and Chandrasekaran [1]. Damage Algorithm and Damage index method used to identify and locate the damage in the composite beam. Modal, Harmonic, and Transient vibration analysis are established to crack identification. Continuous wavelet transform is used to identification of crack in beam like structures by analysing the natural frequency and mode shape of cracked cantilever beam by Rao et al. [2]. Stress intensity factor and strain energy release rates are used to determined elements of stiffness matrix. Natural frequencies and mode shapes are determined by considering beam as continuous to the both side of the crack applying boundary conditions to the characteristic equation of vibration. The crack location can be determined by examining all results.

* Corresponding author. Tel.:+91-8018376761; fax: +91-661-2472926 E-mail address: irshadak85@gmail.com

Available online at www.sciencedirect.com

© 2013 The Authors. Published by Elsevier Ltd. Open access under CC BY-NC-ND license.

Selection and peer-review under responsibility of Institute of Technology, Nirma University, Ahmedabad.

704 Irshad A Khan and Dayal R Parhi / Procedia Engineering 51 ( 2013 ) 703 – 708

Crack localization and sizing in a beam from the free and forced response measurements method is suggested by Karthikeyan et al. [3]. The Timoshenko beam theory is used for modelling transverse vibrations. FEM is used for the free and forced vibration analysis of the cracked beam and open transverse crack is selected for the crack model. The iteration starts with an initial guess for the crack depth ratio and b guesses the crack location and the crack depth until getting the desired convergence for both the crack location and the crack depth. Two Damage identification algorithms are established for assessment of damage using modal test data by Hu et al. [4]. Which are similar in concept to the subspace rotation algorithm or best feasible modal analysis method. Moreover, a quadratic programming model is set up the two methodologies to damage assessments. Salawu [6] has reviewed various methods of damage identification using natural frequencies. The relationship between frequency change and structural damage and vibration monitoring to damage detection are discussed. Pandey et al. [7] is examined a new parameter entitled curvature mode shape, this parameter is used to damage identification in the structures. The change in curvature mode shapes are identifying in region of damage and it can be used to identify damage in structures.

2. Finite Element Analysis

The finite element analysis is brought out for the cracked beams (Cantilever, Fixed-Fixed) to locate the mode shape of transverse vibration at different crack depth. The cracked beams of the current research have the following dimensions. Length of the Beam (L) = 800mm, Width of the beam (W) = 38mm, Height of the Beam (H) = 6mm Relative crack depth = Varies from 0.5mm to 3mm, Relative crack location = at 300mm and 600mm from fixed end Properties for material in analysis:

=0.35, Density= =2.7gm/cc The general purpose finite element software ANSYS is used to the finite element analysis in the frequency domain and obtain natural frequencies, and mode shapes. A higher order 3-D, 10-node element having three degrees of freedom at each node: translations in the nodal x, y, and z directions (Specified as SOLID187 in ANSYS) was selected based on convergence study and used throughout the analysis. Each node has three degrees of freedom, making a total thirty degrees of freedom per element. The Figure (2) represents the detail and Geometry of element SOLID187 and the figure (3) represents First Mode Shape (Cantilever Beam) at Crack depth 1.5mm.

P 1

W

H

L

L 1 L2

P 2

Fig. 1 Geometry Cantilever beam with multiple cracks

Fig. 2 SOLID187, Element Fig. 3 First Mode Shape (Fixed-fixed Beam) at Crack depth 3 mm

705 Irshad A Khan and Dayal R Parhi / Procedia Engineering 51 ( 2013 ) 703 – 708

Figure (4) represent First Mode Shape at crack depth 3 mm and figure (5) represent Second Mode Shape at crack depth 1.5 mm of Cantilever Beam.

3. Experimental Investigation

To validate the Finite element analysis result, an experiment on aluminum beam has been performed. Aluminum cantilever beam and fixed-fixed beam of length 800 mm and cross-section 38 x 6 mm2 was clamped at a vibrating table. Before the experimental study the beams surface has been cleaned and organized for straightness. Subsequently, transverse cracks are created with the help of EDM, which varies from 0.5mm to 3mm at the interval of 0.5 mm. During the experiment the cracked and undamaged beams have been vibrated at their 1st, 2nd and 3rd mode of vibration by using an exciter and a function generator. The vibrations characteristics such as natural frequencies and mode shape of the beams correspond to 1st, 2nd and 3rd mode of vibration have been recorded by placing the accelerometer along the length of the beams and displayed on the vibration indicator. The surface specimens were cut with EDM wire cut machine to ensure high accuracy of cracked model. The experimental results are in close justification with Finite Element Analysis results. Figure (4) represents schematic block diagram of experimental set-up and figure (5) represents view of the experimental set-up.

1. Data acquisition (Accelerometer), 2. Vibration analyser, 3. Vibration indicator embedded with software (Pulse Labshop) 4. Power Distribution, 5. Function generator, 6. Power amplifier, 7. Vibration exciter, 8. Cracked Cantilever beam

Fig. 6 Schematic block diagram of experimental set-up

3

1 4

5

6

8

7

2

Fig. 5 Second Mode Shape (Cantilever Beam) at Crack depth 1.5mm Fig. 4 First Mode Shape (Cantilever Beam) at Crack depth 3 mm

706 Irshad A Khan and Dayal R Parhi / Procedia Engineering 51 ( 2013 ) 703 – 708

4. Results

The variations of frequencies and mode shapes with crack depth for cantilever and fixed-fixed beam for three different modes is plotted in figures 7-18. And it was observed that in all the cases the modal natural frequencies decrease and mode shape increase with increase in crack depth.

Fig. 7 First Mode Nature Frequency versus Crack depth (Cantilever Beam)

Fig. 8 Second Mode Nature Frequency versus Crack depth (Cantilever Beam)

Fig. 9 Third Mode Nature Frequency versus Crack depth (Cantilever Beam)

Fig. 10 First Mode Nature Frequency versus Crack depth (Fixed-Fixed Beam)

Fig. 11 Second Mode Nature Frequency versus Crack depth (Fixed-Fixed Beam)

Fig. 12 Third Mode Nature Frequency versus Crack depth (Fixed-Fixed Beam)

707 Irshad A Khan and Dayal R Parhi / Procedia Engineering 51 ( 2013 ) 703 – 708

Fig. 16 First Mode Shape versus Crack depth (Fixed-Fixed Beam)

Fig. 13 First Mode Shape versus Crack depth (Cantilever Beam)

Fig. 14 Second Mode Shape versus Crack depth (Cantilever Beam)

Fig. 15 Third Mode Shape versus Crack depth (Cantilever Beam)

Fig. 17 Second Mode Shape versus Crack depth (Fixed-Fixed Beam) Fig. 18 Third Mode Shape versus Crack depth

(Fixed-Fixed Beam)

71

71.5

72

72.5

73

73.5

74

74.5

0.5 1 1.5 2 2.5 3

FEAExperimental

1st M

ode

Shap

e (m

m)

Crack Depth (mm)

708 Irshad A Khan and Dayal R Parhi / Procedia Engineering 51 ( 2013 ) 703 – 708

5. Conclusions

The transverse cracks a severe threat to the performance of the structures. It reduces the stiffness of the structures which lead to upset the vibration signatures (Natural frequency and Mode Shape). The present paper ensures to estimate the effects of crack depth on vibration signatures. A finite element analysis and experimental demonstration have been done. It is seen that natural frequencies increase and Mode shapes decrease as the crack depth increases. Experiment and finite results are in good agreement. References [1] Ramanamurthy, E.V.V., Chandrasekaran, K., 2012. Vibration Analysis on a Composite Beam to Identify Damage and Damage Severity using Finite

Element Method, International Journal of Engineering Science and Technology 3, p. 5865. [2] Rao, D.Srinivasa., Rao, K.Mallikarjuna., Raju, G.V., 2010. Crack Identification on a beam by Vibration Measurement and Wavelet Analysis,

International Journal of Engineering Science and Technology 2(5), p. 907. [3] Karthikeyana, M., Tiwaria, R., Talukdar, S., 2007. Crack localisation and sizing in a beam based on the free and forced response measurements,

Mechanical Systems and Signal Processing 21 p. 1362. [4] Hu, N., Wang, X., Fukunaga, H., Yao, Z.H., Zhang, H.X., Wu, Z.S., 2001. Damage Assessment of structures using test data, International Journal of

solids and structures 38, p. 3111. [5] Rizos, P.F., Aspragathos, N., 1990. Identification of Crack Location and Magnitude in a Cantilever Beam from the Vibration Modes, Journal of Sound

and Vibration 138(3), p. 138. [6] Ratcliffe, Colin P., 2000, A Frequency and Curvature Based Experimental Method for Locating Damage in Structures, Journal of Vibration and

Acoustics 122, p. 324. [7] Salawu, O.S., 1997. Detection of Structural Damage thought Changes in frequency: A review, Journal of Engineering Structures 19(9), p. 718. [8] Pandey, A. K., Biswas, M., Samman, M.M., 1990. Damage Detection from changes in curvature Mode Shapes, Journal of Sound and Vibration 145(2), p. 321.