Free vibration response of functionally graded thick plates with shear and normal deformations effects

Composite Structures

Volumn 96, Issue , 2013, Pages 799-823

  Jha, D K ^a   Kant, Tarun ^b   Singh, R K ^a  

^a BHABHA ATOMIC RESEARCH CENTRE   (India)

^b INDIAN INSTITUTE OF TECHNOLOGY BOMBAY   (India)

Author keywords

Free vibration; Functionally graded plates; Higher order shear and normal deformations theory; Material gradient index; Natural frequency; Navier solution

Indexed keywords

FREE VIBRATION; FREE VIBRATION RESPONSE; FUNCTIONALLY GRADED; FUNCTIONALLY GRADED PLATES; HAMILTON'S PRINCIPLE; HIGHER ORDER SHEAR AND NORMAL DEFORMATIONS THEORY; IN-PLANE DISPLACEMENT; MATERIAL DENSITY; MATERIAL GRADIENTS; MATERIAL PROPERTY; NEW SOLUTIONS; NON-LINEAR VARIATION; NUMERICAL SOLUTION; POISSON'S RATIO; POWER-LAW FUNCTIONS; SOLUTION METHODS; SPATIAL COORDINATES; TAYLOR'S SERIES EXPANSION; THEORETICAL MODELS; THICK PLATE; THICKNESS DIRECTION; THREE DIMENSIONAL (3D) ELASTICITY; TRANSVERSE DISPLACEMENTS; TRANSVERSE SHEAR DEFORMATION;

DEFORMATION; EQUATIONS OF MOTION; FUNCTIONALLY GRADED MATERIALS; MECHANICAL PROPERTIES; NATURAL FREQUENCIES; PLATES (STRUCTURAL COMPONENTS); SHEAR FLOW; THREE DIMENSIONAL;

VIBRATIONS (MECHANICAL);

EID: 84870407002     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2012.09.034     Document Type: Article

References (37)

1. Koizumi M. FGM activities in Japan. Composites: Part B 1997, 28:1-4.
2. Suresh S., Mortensen A. Fundamentals of functionally graded materials 1998, IOM Communications, London. 1st ed.
3. Birman V., Byrd L.W. Modeling and analysis of functionally graded materials and structures. ASME Appl Mech Rev 2007, 60:195-216.
4. Jha D.K., Kant Tarun, Singh R.K. A critical review of recent research on functionally graded plates. Compos Struct 2013, 96:833-849.
5. Pagano N.J. Exact solutions for composite laminates in cylindrical bending. J Compos Mater 1969, 3(3):398-411.
6. Pagano N.J. Exact solutions for rectangular bidirectional composites and sandwich plates. J Compos Mater 1970, 4(1):20-34.
7. Srinivas S., Rao A.K. Bending, vibration and buckling of simply supported thick orthotropic plates and laminates. Int J Solids Struct 1970, 6:1463-1481.
8. Srinivas S., Joga Rao C.V., Rao A.K. An exact analysis for vibration of simply supported homogeneous and laminated thick rectangular plates. J Sound Vib 1970, 12:187-199.
9. Pandya B.N., Kant T. Higher-order shear deformable theories for flexure of sandwich plates-finite element evaluations. Int J Solids Struct 1988, 24(12):1267-1286.
10. Kant T., Manjunatha B.S. On accurate estimation of transverse stresses in multilayer laminates. Comput Struct 1994, 50(3):351-365.
11. Reddy J.N. Mechanics of laminated composite plates, theory and analysis 1997, CRC Press, New York. 1st ed.
12. Cheng Z.Q., Batra R.C. Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates. J Sound Vib 2000, 229:879-895.
13. Kim Y.-W. Temperature dependent vibration analysis of functionally graded rectangular plates. J Sound Vib 2005, 284:531-549.
14. Vel S.S., Batra R.C. Three-dimensional exact solution for the vibration of functionally graded rectangular plates. J Sound Vib 2004, 272:703-730.
15. Zenkour A.M. A comprehensive analysis of functionally graded sandwich plates: part 2 - buckling and free vibration. Int J Solids Struct 2005, 42:5243-5258.
16. Ferreira A.J.M., Batra R.C., Roque C.M.C., Qian L.F., Jorge R.M.N. Natural frequencies of functionally graded plates by a meshless method. Compos Struct 2006, 75:593-600.
17. Qian L.F., Batra R.C., Chen L.M. Analysis of cylindrical bending thermoelastic deformations of functionally graded plates by a meshless local Petrov-Galerkin method. Comput Mech 2004, 33:263-273.
18. Prakash T., Ganapathi M. Asymmetric flexural vibration and thermoelastic stability of FGM circular plates using finite element method. Composites: Part B 2006, 37:642-649.
19. Bhangale R.K., Ganesan N. Free vibration of simply supported functionally graded and layered magneto-electro-elastic plates by finite element method. J Sound Vib 2006, 294:1016-1038.
20. Matsunaga H. Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory. Compos Struct 2008, 82:499-512.
21. Ebrahimi F., Rastgoo A. An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory. Thin-Wall Struct 2008, 46:1402-1408.
22. 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.
23. Shahrjerdi A., Mustapha F., Bayat M., Sapuan S.M., Zahari R., Shahzamanian M.M. Natural frequency of F.G. rectangular plate by shear deformation theory. IOP Conf Ser: Mater Sci Eng 2011, 17(1):1-6.
24. Kumar J.S., Reddy B.S., Reddy C.E., Reddy K.V.K. Higher order theory for free vibration analysis of functionally graded material plates. ARPN J Eng Appl Sci 2011, 6:105-111.
25. Benachour A., Tahar H.D., Atmane H.A., Tounsi A., Ahmed M.S. A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient. Composites: Part B 2011, 42:1386-1394.
26. Xiang S., Jin Y.X., Bi Z.Y., Jiang S.X., Yang M.S. A n-order shear deformation theory for free vibration of functionally graded and composite sandwich plates. Compos Struct 2011, 93:2826-2832.
27. Neves A.M.A., Ferreira A.J.M., Carrera E., Roque C.M.C., Cinefra M., Jorge R.M.N., et al. A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates. Composites: Part B 2012, 43:711-725.
28. Neves A.M.A., Ferreira A.J.M., Carrera E., Roque C.M.C., Cinefra M., Jorge R.M.N., et al. A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates. Compos Struct 2012, 94(5):1814-1825.
29. Whitney J.M., Pagano N.J. Shear deformation in heterogeneous anisotropic plates. ASME J Appl Mech 1970, 37:1031-1036.
30. Timoshenko S.P., Woinowsky-Krieger S. Theory of plates and shells 1959, McGraw-Hill, Singapore. 2nd edn.
31. Timoshenko S.P., Goodier J.N. Theory of elasticity 1970, McGraw-Hill, Singapore. 3rd international edn.
32. Praveen G.N., Reddy J.N. Nonlinear transient thermoelastic analysis of functionlly graded ceramic-metal plates. Int J Solids Struct 1998, 35:4457-4471.
33. Senthilnathan N.R., Lim K.H., Lee K.H., Chow S.T. Buckling of shear-deformable plates. AIAA J 1987, 25:1268-1271.
34. Shimpi R.P. Refined plate theory and its variants. AIAA J 2002, 40:137-146.
35. Shimpi R.P., Patel H.G. A two variable refined plate theory for orthotropic plate analysis. Int J Solids Struct 2006, 43:6783-6799.
36. Reisman H., Lee Y.C. Forced motions of rectangular plates. Develop Theor Appl Mech 1969, 4:3.
37. Kant T, Reddy SK. Private communication; 2012.