Exact 3-D Solution for Free Bending Vibration of Thick FG Plates and Homogeneous Plate Coated by a Single FG Layer on Elastic Foundations
محورهای موضوعی : Engineering
H Salehipour
1
(School of Mechanical Engineering, Isfahan University of Technology)
R Hosseini
2
(School of Mechanical Engineering, University of Tehran)
K Firoozbakhsh
3
(School of Mechanical Engineering, Sharif University of Technology)
کلید واژه: Free bending vibration, Exact 3-D solution, Thick FG plates, Homogeneous plate coated by a single FG layer, Winkler-Pasternak elastic foundation,
چکیده مقاله :
This paper presents new exact 3-D (three-dimensional) elasticity closed-form solutions for out-of-plane free vibration of thick rectangular single layered FG (functionally graded) plates and thick rectangular homogeneous plate coated by a functionally graded layer with simply supported boundary conditions. It is assumed that the plate is on a Winkler-Pasternak elastic foundation and elasticity modulus and mass density of the FG layer vary exponentially through the thickness of the FG layer, whereas Poisson’s ratio is constant. In order to solve the equations of motion, a proposed displacement field is used for each layer. Influences of stiffness of the foundation, inhomogeneity of the FG layer and coating thickness-to-total thickness ratio on the natural frequencies of the plates are discussed. Numerical results presented in this paper can serve as benchmarks for future vibration analyses of single layered FG plates and coated plates on elastic foundations.
[1] Yamanouchi M., Koizumi M., Hirai T., Shiota I., 1990, Functionally gradient materials forum, Proceedings of First International Symposium on Functionally Gradient Materials, Sendai, Japan.
[2] Koizumi M., 1993, Functional gradient material, Ceramic Transactions 34:3-10.
[3] Tarn J.Q., Wang Y. M., 1994, A three- dimensional analyses of anisotropic inhomogeneous and laminated plates, Journal of Thermal Stresses 31:497-515.
[4] Tarn J.Q., Wang Y. M., 1995, Asymptotic thermoelastic analyses of anisotropic inhomogeneous and laminated plates, Journal of Thermal Stresses 18:35-38.
[5] Chen W.Q., Ding H. J., 2000, Bending of functionally graded piezoelectric rectangular plates, Acta Mechanica Solida Sinica 13:312-319.
[6] Chen W.Q., Lee K.Y., Ding H. J., 2005, On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates, Journal of Sound and Vibration 279:237-251.
[7] Reddy J.N., Cheng Z.Q., 2001, Three-dimensional solutions of smart functionally graded plates, Journal of Applied Mechanics 68:234-241.
[8] Vel S.S., Batra R.C.,2002, Exact solution for thermoelastic deformations of functionally graded thick rectangular plates, American Institute of Aeronautics and Astronautics 40:1421-1433.
[9] Vel S.S., Batra R.C.,2003, Three-dimensional analysis of transient thermal stresses in functionally graded plates, International Journal of Solids and Structures 40:7181-7196.
[10] Vel S.S., Batra R.C., 2004, Three-dimensional exact solution for the vibration of functionally graded rectangular plates, Journal of Sound and Vibration 272:703-730.
[11] Zhong Z., Shang E.T., 2003, Three-dimensional exact analysis of a simply supported functionally gradient piezoelectric plate, International Journal of Solids and Structures 40:5335-5352.
[12] Zhong Z., Yu T., 2006, Vibration of simply supported functionally graded piezoelectric rectangular plate, Smart Materials and Structures 15:1404-1412.
[13] Kashtalyan M., Menshykova M., 2007, Three-dimensional elastic deformation of a functionally graded coating/substrate system, International Journal of Solids and Structures 44:5272-5288.
[14] Kashtalyan M., Menshykova M., 2009, Effect of a functionally graded interlayer on three-dimensional elastic deformation of coated plates subjected to transverse loading, Composite Structures 89:167-176.
[15] Kashtalyan M., 2004, Three-dimensional elasticity solution for bending of functionally graded rectangular plates, European Journal of Mechanics - A/Solids 23:853-864.
[16] Huang Z.Y., Lu C.F., Chen W.Q., 2008, Benchmark solutions for functionally graded thick plates resting on Winkler–Pasternak elastic foundations, Composite Structures 85:95-104.
[17] Lu C.F., Chen W.Q., Shao J.W., 2008, Semi-analytical three-dimensional elasticity solutions for generally laminated composite plates, European Journal of Mechanics - A/Solids 27:899-917.
[18] Lu C.F., Lim C.W., Chen W.Q., 2009, Exact solutions for free vibration of functionally graded thick plates on elastic foundations, Mechanics of Advanced Materials and Structures 16:576-584.
[19] Li Q., Iu V.P., Kou K.P., 2008, Three-dimensional vibration analysis of functionally graded material sandwich plates, Journal of Sound and Vibration 311:498-515.
[20] Li Q., Iu V.P., Kou K.P., 2009, Three-dimensional vibration analysis of functionally graded material plates in thermal environment, Journal of Sound and Vibration 324:733-750.
[21] Amini M.H., Soleimani M., Rastgoo A., 2009, Three-dimensional free vibration analysis of functionally graded material plates resting on an elastic foundation, Smart Materials and Structures 18:1-9.
[22] Alibeigloo A., 2010, Exact solution for thermo-elastic response of functionally graded rectangular plates, Composite Structures 92:113-121.
[23] Hosseini-Hashemi S.h., Salehipour H., Atashipour S.R., 2012, Exact three-dimensional free vibration analysis of thick homogeneous plates coated by a functionally graded layer, Acta Mechanica 223:2153-2166.
[24] Hosseini-Hashemi S.h., Salehipour H., Atashipour S.R., Sburlati R., 2013, On the exact in-plane and out-of-plane free vibration analysis of thick functionally graded rectangular plates: Explicit 3-D elasticity solutions, Composites Part B 46:108-115.
[25] Levinson M., 1984, A novel approach to thick plate theory suggested by studies in foundation theory, International Journal of Mechanical Sciences 26:427-436.
[26] Levinson M., 1985, The simply supported rectangular plate: an exact, three dimensional, linear elasticity solution, Journal of Elasticity 15:283-291.
[27] Levinson M., 1985, Free vibrations of a simply supported, rectangular plate: an exact elasticity, Journal of Sound and Vibration 98:289-298.
