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Koizumi M (1993) The concept of FGM. Ceram Trans 34:3–10 Zhong Z, Wu LZ, Cheng WQ (2010) Progress in the study on mechanics problems of functionally graded materials and structures. Adv Mech 40:528–541 Chakraborty A, Gopalakrishnan S (2004) Wave propagation in inhomogeneous layered media: solution of forward and inverse problems. Acta Mech 169:153–185 Praveen GN, Reddy JN (1998) Nonlinear transient thermoelastic analysis of FGM ceramic–metal plates. Int J Solids Struct 35:4457–4476 Tanigawa Y, Matsumoto M, Akat T (1996) Optimization problem of material composition for nonhomogeneous plate to minimize thermal stress. Trans JSME Ser A 62:115–122 Wang S, Ni CY, Zhu XX (2005) Temperature field analysis for heterogeneous material piston. J Beijing Univ Aeronaut Astronaut 31:1299–1302 Cheng ZQ, Batra RC (2000) 3-D thermoelastic deformations of a FGM elliptic plate. Compos B 31:97–106 Zhou FX, Li SR (2009) Three-dimensional analysis for transient thermal responses of functionally graded rectangular plate. Eng Mech 26:59–64 Zhong Z, Yu T (2006) Two-dimensional analysis of functionallygraded beams. AIAA J 44:3160–3164 Zheng L, Zhong Z (2009) Exact solution for axisymmetric bending of functionally graded circular plate under elastically supported boundary condition. J Tongji Univ 37:893–897 Guo LC, Noda N (2007) Modeling method for a crack problem of functionally graded materials with arbitrary properties piecewise-exponential model. Int J Solids Struct 44:6768–6790 Choi HJ (1996) Bonded dissimilar strips with a crack perpendicular to the functionally graded interface. Int J Solids Struct 33:4101–4117 Guo LC, Wu LZ, Zeng T, Ma L (2004) Mode I crack problem for a functionally graded orthotropic strip. Eur J Mech A-Solid 23:219–234 Du CC, Li YH (2010) Free vibration of functionally graded cylindrical thin shells. J Dyn Control 8:219–223 Tornabene F (2009) Free vibration analysis of functionally graded conical, cylindrical and annular shell structures with a four-parameter power-law distribution. Comput Method Appl Mech 198:2911–2935 Chen WQ, Bian ZG, Lv CF (2004) 3D Free vibration analysis of a functionally graded piezoelectric hollow cylinder filled with compressible fluid. Int J Solids Struct 41:947–964 Nie GJ, Zhong Z (2008) Vibration analysis of functionally graded annular sectorial plates with simply supported radial edges. Compos Struct 84:167–176 Qian Z, Jin F, Lu T (2009) Transverse surface waves in an FGM layered structure. Acta Mech 207:183–193 Samadhiya R, Mukherjee A, Schmauder S (2006) Characterization of discretely graded materials using acoustic wave propagation. Comp Mater Sci 37:20–28 Cao ZY, Cheng HM (2007) Micro-element model for three-dimensional analysis of functionally graded structures. Chin J Comput Mech 24:392–396 Tornabene F, Viola E, Inmand J (2009) 2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures. J Sound Vib 328:259–290 Abu-alshaikh I, Köklüce B (2006) One dimensional transient dynamic response in functionally graded layered media. J Eng Math 54:17–30 Lu JF, Guan Y (2004) Numerical solution of partial differential equations, China. Tsinghua University Press, Beijing, pp 107–111 Kachanov LM (1986) Introduction to continuum damage mechanics. Martinus Nijhoff Publishers, Dordrecht Cheng HM, Cao ZY (2007) The study on wave propagation characters in damaged media. Chin Q Mech 26:177–183 Wang LL (2005) Foundation of stress waves, China. National Defense Industry Press, Beijing Kennett BLN (1981) Elastic wave propagation in stratified media. Adv Appl Mech 21:79–164 Guo WG, Li YL, Suo T (2007) Concise course on stress waves foundation, China. Publishing House of Electronics Industry, Beijing