Assessment of Voigt and Mori-Tanaka models for vibration analysis of functionally graded plates

Composite Structures

Volumn 94, Issue 7, 2012, Pages 2197-2208

  Shen, Hui Shen ^a,b   Wang, Zhen Xin ^a  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

^b Shanghai Jiao Tong University   (China)

Author keywords

Functionally graded materials; Mori Tanaka model; Nonlinear vibration; Pasternak elastic foundation; Temperature dependent properties; Voigt model

Indexed keywords

MORI-TANAKA MODELS; NONLINEAR VIBRATION; PASTERNAK ELASTIC FOUNDATIONS; TEMPERATURE-DEPENDENT PROPERTIES; VOIGT MODEL;

EQUATIONS OF MOTION; FUNCTIONALLY GRADED MATERIALS; PLATES (STRUCTURAL COMPONENTS); THERMAL EFFECTS;

VIBRATION ANALYSIS;

EID: 84862798544     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2012.02.018     Document Type: Article

References (33)

1. Lü C.F., Lim C.W., Chen W.Q. Exact solutions for free vibrations of functionally graded thick plates on elastic foundations. Mech Adv Mater Struct 2009, 16:576-584.
2. Liu D.Y., Wang C.Y., Chen W.Q. Free vibration of FGM plates with in-plane material inhomogeneity. Compos Struct 2010, 92:1047-1051.
3. Kitipornchai S., Yang J., Liew K.M. Random vibration of the functionally graded laminates in thermal environments. Comput Methods Appl Mech Eng 2006, 195:1075-1095.
4. Yang J., Kitipornchai S., Liew K.M. Large amplitude vibration of thermoelectric-mechanically stressed FGM laminated plates. Comput Methods Appl Mech Eng 2003, 192:3861-3885.
5. Huang X.-L., Shen H.-S. Nonlinear vibration and dynamic response of functionally graded plates in thermal environments. Int J Solids Struct 2004, 41:2403-2427.
6. Huang X.-L., Shen H.-S. Vibration and dynamic response of functionally graded plates with piezoelectric actuators in thermal environments. J Sound Vib 2006, 289:25-53.
7. Xia X.-K., Shen H.-S. Nonlinear vibration and dynamic response of FGM plates with piezoelectric fiber reinforced composite actuators. Compos Struct 2009, 90:254-262.
8. Fakhari V., Ohadi A., Yousefian P. Nonlinear free and forced vibration behavior of functionally graded plate with piezoelectric layers in thermal environment. Compos Struct 2010, 93:2310-2321.
9. Sundararajan N., Prakash T., Ganapathi M. Nonlinear free flexural vibrations of functionally graded rectangular and skew plates under thermal environments. Finite Elem Anal Des 2005, 42:152-168.
10. Chen C.S. Nonlinear vibration of a shear deformable functionally graded plate. Compos Struct 2005, 68:295-302.
11. Chen C.S., Chen T.J., Chien R.-D. Nonlinear vibration of initially stressed functionally graded plates. Thin-Walled Struct 2006, 44:844-851.
12. Fung C.P., Chen C.S. Imperfection sensitivity in the nonlinear vibration of functionally graded plates. Eur J Mech A - Solids 2006, 25:425-436.
13. Chen C.S., Tan A.H. Imperfection sensitivity in the nonlinear vibration of initially stresses functionally graded plates. Compos Struct 2007, 78:529-536.
14. Chen C.S., Fung C.P., Yu S.Y. The investigation on the vibration and stability of functionally graded plates. J Reinf Plast Compos 2008, 27:1435-1447.
15. Chen C.S., Hsu C.Y., Tzou G.J. Vibration and stability of functionally graded plates based on a higher-order deformation theory. J Reinf Plast Compos 2009, 28:1215-1234.
16. Mao Y.Q., Fu Y.M. Nonlinear dynamic response and active vibration control for piezoelectric functionally graded plate. J Sound Vib 2010, 329:2015-2028.
17. Talha M., Singh B.N. Large amplitude free flexural vibration analysis of shear deformable FGM plates using nonlinear finite element method. Finite Elem Anal Des 2011, 47:394-401.
18. Shen H.-S. Functionally graded materials nonlinear analysis of plates and shells 2009, CRC Press, Boca Raton.
19. Huang C.S., McGee O.G., Chang M.J. Vibrations of cracked rectangular FGM thick plates. Compos Struct 2011, 93:1747-1764.
20. Reddy J.N. A refined nonlinear theory of plates with transverse shear deformation. Int J Solids Struct 1984, 20:881-896.
21. Shen H.-S. Kármán-type equations for a higher-order shear deformation plate theory and its use in the thermal postbuckling analysis. Appl Math Mech 1997, 18:1137-1152.
22. Reddy J.N., Chin C.D. Thermomechanical analysis of functionally graded cylinders and plates. J Therm Stress 1998, 21:593-629.
23. Touloukian Y.S. Thermophysical properties of high temperature solid materials 1967, Macmillan, New York.
24. Gibson L.J., Ashby M.F., Karam G.N., Wegst U., Shercliff H.R. Mechanical properties of natural materials. II. Microstructures for mechanical efficiency. Proc Roy Soc Lond A 1995, 450:141-162.
25. Mori T., Tanaka K. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 1973, 2:1571-1574.
26. Hill R. A self-consistent mechanics of composite materials. J Mech Phys Solids 1965, 13:213-222.
27. Shen H.-S., Yang J., Zhang L. Free and forced vibration of Reissner-Mindlin plates with free edges resting on elastic foundations. J Sound Vib 2001, 244:299-320.
28. Shen H.-S., Wang Z.-X. Nonlinear bending of FGM plates subjected to combined loading and resting on elastic foundations. Compos Struct 2010, 92:2517-2524.
29. Shen H.-S. Nonlinear thermal bending response of FGM plates due to heat conduction. Composites Part B 2007, 38:201-215.
30. Bishop R.E.D. The mechanics of vibration 1979, Cambridge University Press, New York.
31. He X.Q., Ng T.Y., Sivashanker S., Liew K.M. Active control of FGM plates with integrated piezoelectric sensors and actuators. Int J Solids Struct 2001, 38:1641-1655.
32. Kitipornchai S., Yang J., Liew K.M. Random vibration of the functionally graded laminates in thermal environments. Comput Methods Appl Mech Eng 2006, 195:1075-1095.
33. Park J.S., Kim J.H. Thermal postbuckling and vibration analyses of functionally graded plates. J Sound Vib 2006, 289:77-93.