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Mode shape analysis of multiple cracked functionally graded beam-like structures by using dynamic stiffness method

Tran Van Lien, Ngo Trong Duc, Nguyen Tien Khiem

Abstract


Mode shapes of multiple cracked beam-like structures made of Functionally Graded Material (FGM) are analyzed by using the dynamic stiffness method. Governing equations in vibration theory of multiple cracked FGM beam are derived on the base of Timoshenko beam theory; power law variation of material; coupled spring model of crack and taking into account the actual position of neutral axis. A general solution of vibration in frequency domain is obtained and used for constructing dynamic stiffness matrix of the multiple cracked FGM Timoshenko beam element that provides an efficient method for modal analysis of multiple cracked FGM frame structures. The theoretical development is illustrated by numerical analysis of crack-induced change in mode shapes of multi-span continuous FGM beam.

Keywords


FGM; multiple cracked beam; modal analysis; dynamic stiffness method

References


B. H. Wu. The surface crack problem for a plate with functionally graded properties. Journal of Applied Mechanics, 64, (1997), pp. 449–456. doi:10.1115/1.2788914.

A. S. J. Swamidas, X. Yang, and R. Seshadri. Identification of cracking in beam structures using Timoshenko and Euler formulations. Journal of Engineering Mechanics, 130, (11), (2004), pp. 1297–1308. doi:10.1061/(asce)0733-9399(2004)130:11(1297).

J. Yang and Y. Chen. Free vibration and buckling analyses of functionally graded beams with edge cracks. Composite Structures, 83, (1), (2008), pp. 48–60. doi:10.1016/j.compstruct.2007.03.006.

L. L. Ke, J. Yang, S. Kitipornchai, and Y. Xiang. Flexural vibration and elastic buckling of a cracked Timoshenko beam made of functionally graded materials. Mechanics of Advanced Materials and Structures, 16, (6), (2009), pp. 488–502. doi:10.1080/15376490902781175.

K. Aydin. Free vibration of functionally graded beams with arbitrary number of surface cracks. European Journal of Mechanics-A/Solids, 42, (2013), pp. 112–124. doi:10.1016/j.euromechsol.2013.05.002.

D. Wei, Y. Liu, and Z. Xiang. An analytical method for free vibration analysis of functionally graded beams with edge cracks. Journal of Sound and Vibration, 331, (7), (2012), pp. 1686–1700. doi:10.1016/j.jsv.2011.11.020.

K. Sherafatnia, G. Farrahi, and S. A. Faghidian. Analytic approach to free vibration and buckling analysis of functionally graded beams with edge cracks using four engineering beam theories. International Journal of Engineering-Transactions C: Aspects, 27, (6), (2013), pp. 979–990. doi:10.5829/idosi.ije.2014.27.06c.17.

T. Yan, S. Kitipornchai, J. Yang, and X. Q. He. Dynamic behaviour of edge-cracked shear deformable functionally graded beams on an elastic foundation under a moving load. Composite Structures, 93, (11), (2011), pp. 2992–3001. doi:10.1016/j.compstruct.2011.05.003.

S. Kitipornchai, L. L. Ke, J. Yang, and Y. Xiang. Nonlinear vibration of edge cracked functionally graded Timoshenko beams. Journal of Sound and Vibration, 324, (3), (2009), pp. 962–982. doi:10.1016/j.jsv.2009.02.023.

N. Wattanasakulpong and V. Ungbhakorn. Free vibration analysis of functionally graded beams with general elastically end constraints by DTM. World Journal of Mechanics, 2, (06), (2012), pp. 297–310. doi:10.4236/wjm.2012.26036.

S. D. Akbas. Free vibration characteristics of edge cracked functionally graded beams by using finite element method. International Journal of Engineering Trends and Technology, 4, (10), (2013), pp. 4590–4597.

Z. Yu and F. Chu. Identification of crack in functionally graded material beams using the p-version of finite element method. Journal of Sound and Vibration, 325, (1), (2009), pp. 69–84. doi:10.1016/j.jsv.2009.03.010.

A. Banerjee, B. Panigrahi, and G. Pohit. Crack modelling and detection in Timoshenko FGM beam under transverse vibration using frequency contour and response surface model with GA. Nondestructive Testing and Evaluation, 31, (2), (2016), pp. 142–164. doi:10.1080/10589759.2015.1071812.

N. T. Khiem and N. N. Huyen. A method for crack identification in functionally graded Timoshenko beam. Nondestructive Testing and Evaluation, 32, (3), (2017), pp. 319–341. doi:10.1080/10589759.2016.1226304.

H. Su, J. R. Banerjee, and C. W. Cheung. Dynamic stiffness formulation and free vibration analysis of functionally graded beams. Composite Structures, 106, (2013), pp. 854–862. doi:10.1016/j.compstruct.2013.06.029.

H. Su and J. R. Banerjee. Development of dynamic stiffness method for free vibration of functionally graded Timoshenko beams. Computers & Structures, 147, (2015), pp. 107–116. doi:10.1016/j.compstruc.2014.10.001.

N. T. Khiem, N. D. Kien, and N. N. Huyen. Vibration theory of FGM beam in the frequency domain. In Proceedings of National Conference on Engineering Mechanics celebrating 35th Anniversary of the Institute of Mechanics, VAST, Vol. 1, (2014), pp. 93–98. (in Vietnamese).

T. V. Lien, N. T. Khiem, and N. T. Duc. Free vibration analysis of functionally graded Timoshenko beam using dynamic stiffness method. Journal of Science and Technology in Civil Engineering, (31), (2016), pp. 19–28.

T. G. Chondros, A. D. Dimarogonas, and J. Yao. Longitudinal vibration of a continuous cracked bar. Engineering Fracture Mechanics, 61, (5), (1998), pp. 593–606. doi:10.1016/s0013- 7944(98)00071-x.

T. G. Chondros, A. D. Dimarogonas, and J. Yao. A continuous cracked beam vibration theory. Journal of Sound and Vibration, 215, (1), (1998), pp. 17–34. doi:10.1006/jsvi.1998.1640.


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