Double Cracks Identification in Functionally Graded Beams Using Artificial Neural Network

Document Type: Research Paper

Authors

1 Department of Mechanical Engineering, Ferdowsi University of Mashhad

2 Department of Mechanical Engineering, Lean Production Engineering Research Center, Ferdowsi University of Mashhad

Abstract

This study presents a new procedure based on Artificial Neural Network (ANN) for identification of double cracks in Functionally Graded Beams (FGBs). A cantilever beam is modeled using Finite Element Method (FEM) for analyzing a double-cracked FGB and evaluation of its first four natural frequencies for different cracks depths and locations. The obtained FEM results are verified against available references. Furthermore, four Multi-Layer Perceptron (MLP) neural networks are employed for identification of locations and depths of both cracks of FGB. Back-Error Propagation (BEP) method is used to train the ANNs. The accuracy of predicted results shows that the proposed procedure is suitable for double cracks identification detection in FGBs.

Keywords

 [1] Douka E., Loutridis S., Trochidis A., 2003, Crack identification in beams using wavelet analysis, International Journal of Solid Structures 40(13-14): 3557-3569.

[2] Dimarogonas A.D., 1996, Vibration of cracked structures: A state of the art review, Engineering Fracture Mechanic

55(5): 831-857.

[3] Dimarogonas A.D., 1976, Vibration Engineering, West Publishers, St Paul, Minnesota.

[4] Paipetis S.A., Dimarogonas A.D., 1986, Analytical Methods in Rotor Dynamics, Elsevier Applied Science, London.

[5] Adams A.D., Cawley P., 1979, The location of defects in structures from measurements of natural frequencies, Journal of Strain Analysis for Engineering Design14(2): 49-57.

[6] Chondros T.G., Dimarogonas A.D., 1980, Identification of cracks in welded joints of complex structures, Journal of Sound and Vibration 69(11): 531-538.

[7] Goudmunson P., 1982, Eigen frequency change of structures: a state of the art review, Engineering Fracture Mechanic 55(5): 831-857.

[8] Shen M.H.H., Taylor J.E., 1991, An identification problem for vibrating cracked beams, Journal of Sound and Vibration 150(3): 457-484.

[9] Masoud A., Jarrad M.A., Al-Maamory M., 1998, Effect of crack depth on the natural frequency of a prestressed fixed-fixed beam, Journal of Sound and Vibration 214(2): 201-212.

[10] Sekhar A.S., 2008, Multiple cracks effects and identification, Journal of Mechanical Systems and Signal Processing 22(4): 845-878.

[11] Lee J., 2009, Identification of multiple cracks in a beam using natural frequencies, Journal of Sound and Vibration 320(3): 482-490.

[12] Patil D.P., Maiti S.K., 2003, Detection of multiple cracks using frequency measurements, Engineering Fracture Mechanic 70(12): 1553-1572.

[13] Mazanoglu K., Yesilyurt I., Sabuncu M., 2009, Vibration analysis of multiple-cracked non-uniform beams, Journal of Sound and Vibration 320(4-5): 977-989.

[14] Binici B., 2005, Vibration of beams with multiple open cracks subjected to axial force, Journal of Sound and Vibration 287(1-2): 277-295.

[15] Khiem N.T., Lien T.V., 2001, A simplified method for natural frequency analysis of a multiple cracked beam, Journal of Sound and Vibration 245(4): 737-751.

[16] Cam E., Sadettin O., Murat L., 2008, An analysis of cracked beam structure using impact echo method, Independent Nondestructive Testing and Evaluation 38(5): 368-373.

[17] Wu X., Ghaboussi J., Garret Jr J.H., 1992, Use of neural networks in detection of structural damage, Computers and Structures 42(4): 649-659.

[18] Wang B.S., He Z.C., 2007, Crack detection of arch dam using statistical neural network based on the reductions of natural frequencies, Journal of Sound and Vibration 302(4-5): 1037-1047.

[19] Kao C.Y., Hung S.L., 2003, Detection of structural damage via free vibration responses generated by approximating artificial neural networks, Computers and Structures 81(28-29): 2631-2644.

[20] Chen Q., Chan Y.W., Worden K., 2003, Structural fault diagnosis and isolation using neural networks based on response-only data, Computers and Structures 81(22-23): 2165-2172.

[21] Yu Z., Chu F., 2009, Identification of crack in functionally graded material beams using the p-version of finite element method, Journal of Sound and Vibration 325(1-2): 69-84.

[22] Kitipornchai S., Ke L.L, Yang J., Xiang Y., 2009, Nonlinear vibration of edge cracked functionally graded Timoshenko beams, Journal of Sound and Vibration 324(3-5): 962-982.

[23] Yang J., Chen Y., 2008, Free vibration and buckling analyses of functionally graded beams with edge cracks, Computers and Structures 83(1): 48-60.

[24] Simsek M., 2010, Non-linear vibration analysis of a functionally graded Timoshenko beam under action of a moving harmonic load, Computers and Structures 92(10): 2532-2546.

[25] Broek D., 1986, Elementary Engineering Fracture Mechanics, Martinus Nijhoff Publishers, Dordrecht.

[26] Erdogan F., Wu B.H., 1997, The surface crack problem for a plate with functionally graded properties, Journal of Applied Mechanics 64(3): 448-456.

[27] Yang J., Chen Y., Xiang Y., Jia X.L., 2008, Free and forced vibration of cracked inhomogeneous beams under an axial force and a moving load, Journal of Sound and Vibration 312(1-2): 166-181.

[28] ANSYS Release 8.0. ANSYS, Inc. Southpointe 275 Technology Drive Canonsburg, PA 15317.

[29] Wu J.D., Chan. J.J., 2009, Faulted gear identification of a rotating machinery based on wavelet transform and artificial neural network, Expert Systems with Applications 36:8862-8875.

[30] McClelland J.L., Rumelhart D.E., 1986, Explorations in the Microstructure of Cognition, Parallel Distributed Processing: Vol.I and II, MIT Press.

[31] The Math works Inc, Version 2009, MATLAB.