Three-dimensional Free Vibration Analysis of a Transversely Isotropic Thermoelastic Diffusive Cylindrical Panel

Subject Areas : Engineering

R Kumar ¹ , T Kansal ²

1 - Department of Mathematics, Kurukshetra University
2 - Department of Mathematics, Kurukshetra University

Received: 2010-10-04 Accepted : 2010-12-23 Published : 2010-12-30

Keywords:

References:

[1] Aouadi M., 2007, Uniqueness and reciprocity theorems in the theory of generalized thermoelastic diffusion, Journal of Thermal Stresses 30: 665-678.

[2] Aouadi M., 2008, Generalized theory of thermoelastic diffusion for anisotropic media, Journal of Thermal Stresses 31: 270-285.

[3] Bert C.W., Baker J.K., Egle D.M., 1969, Free vibrations of multilayer anisotropic cylindrical shells, Journal of Composite Materials 3: 1173-1186.

[4] Buchwald V.P., 1961, Rayleigh waves in transversely isotropic media, Quarterly Journal of Mechanics and Applied Mathematics, 14: 193-304.

[5] Chau K.T., 1994, Vibrations of transversely isotropic circular cylinders, ASME Journal of Applied Mechanics 61: 964-970.

[6] Fan J.R.., Ding K.W., 1993, Analytical solution for thick closed laminated cylindrical shells, International Journal of Mechanical Sciences 35: 657-668.

[7] Gawinecki J.A.., Kacprzyk P., Bar-Yoseph P., 2000, Initial boundary value problem for some coupled nonlinear parabolic system of partial differential equations appearing in thermoelastic diffusion in solid body, J. Anal. Appl, 19: 121-130.

[8] Gawinecki J. A., Szymaniec A., 2002, Global solution of the cauchy problem in nonlinear thermoelastic diffusion in solid body, Proceedings in Applied Mathematics and Mechanics 1: 446-447.

[9] Green A.E., Lindsay K.A., 1972, Thermoelasticity, Journal of Elasticity 2: 1-7.

[10] Ip K.H., Chan W.K., Tse P.C., Lai T.C., 1996, Vibration analysis of orthotropic cylindrical shells with free ends by Rayleigh-Ritz method, Journal of Sound and Vibration 195: 117-135.

[11] Jiang X.Y.,1997, 3-D vibration analysis of fiber reinforced composite laminated cylindrical shells, Journal of Vibration and Acoustics 119: 46-51.

[12] Jones R.M., Margan H., 1975, Buckling and vibration of cross ply laminated circular cylindrical shells, AIAA Journal 13: 664-671.

[13] Kumar R., Kansal T., 2008, Propagation of lamb waves in transversely isotropic thermoelastic diffusive plate, International Journal of Solids and Structures 45: 5890-5913.

[14] Lord H.W., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of Mechanics and Physics of Solids 15: 299-309.

[15] Mirsky I., 1965, Wave propagation in transversely isotropic circular cylinders (part I and II), Journal of the Acoustical Society of America 37: 1016-1026.

[16] Nowacki W., 1974, Dynamical problems of thermodiffusion in solids-I, Bulletin of Polish Academy of Sciences Series, Science and Technology 22: 55- 64.

[17] Nowacki W., 1974, Dynamical problems of thermodiffusion in solids-II, Bulletin of Polish Academy of Sciences Series, Science and Technology 22: 129-135.

[18] Nowacki W., 1974,Dynamical problems of thermodiffusion in solids-III, Bulletin of Polish Academy of Sciences Series, Science and Technology 22: 257-266.

[19] Nowacki W., 1976, Dynamical problems of thermodiffusion in solids, Engineering Fracture Mechanics 8: 261-266.

[20] Sharma J.N., Sharma P.K., 2002, Free vibration analysis of homogeneous transversely isotropic thermoelastic cylindrical panel, Journal of Thermal Stresses 25: 169-182.

[21] Sherief H.H., Hamza F., Saleh H., 2004, The theory of generalized thermoelastic diffusion, International Journal of Engineering Science 42: 591- 608.

[22] Sherief H.H., Saleh H., 2005, A half space problem in the theory of generalized thermoelastic diffusion, International Journal of Solids and Structures 42: 4484-4493.

[23] So J.Y., Leissa A.W., 1997, Free vibrations of thick hollow cylinders from three dimensional analysis, Journal of Vibration and Acoustics 119: 89-95.

[24] Soedel W., 1983, Simplified equations and solutions for the vibration of orthotropic cylindrical shells, Journal of Sound and Vibration 87: 555-566.

[25] Soldatos K.P., 1987, Influence of thickness shear deformation on free vibrations of rectangular plates and cylinders of antisymmetric angle ply construction, Journal of Sound and Vibration 119: 111-137.

[26] Soldatos K.P., Hadhgeorgian V.P., Three-dimensional solutions of the free vibration problem of homogeneous isotropic cylindrical shells and panels, Journal of Sound and Vibration 137: 369-384.

[27] Ye J.Q., Soldatos K.P., 1994, 3-D vibrations of laminated cylinders and cylindrical panels with symmetric and antisymmetric cross-ply layup, Composites part B: Engineering 4: 429-444.