Effects of Geometric Nonlinearity on Stress Analysis in Large Amplitude Vibration of Moderately Thick Annular Functionally Graded Plate

Journal of Solid Mechanics

مقاله 6، دوره 1، شماره 4، اسفند 2009، صفحه 328-342   

نوع مقاله: Research Paper

نویسندگان

M.H Amini^* ؛ A Rastgoo؛ M Soleimani

Faculty of Mechanical Engineering, College of Engineering, University of Tehran

چکیده

This paper deals with the nonlinear free vibration of thick annular functionally graded material plates. The thickness is assumed to be constant. Material properties are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The formulations are based on the first-order shear deformation plate theory and von Kármán-type equation. For harmonic vibrations, by using assumed-time-mode method sinusoidal oscillations are assumed, then the time variable is eliminated by applying Kantorovich averaging method. Thus, the basic governing equations for the problem are reduced to a set of ordinary differential equations in term of radius. The results reveal that vibration amplitude and volume fraction have significant effects on the resultant stresses in large amplitude vibration of the functionally graded thick plate.

کلیدواژه‌ها

Functionally graded material؛ Large amplitude vibration؛ Stress Analysis؛ Thick annular plate

مراجع

[1] Bhimaraddi A., Chandrashekhara K., 1993, Nonlinear vibrations of heated antisymmetric angle-ply laminated plates, International Journal of Solids and Structures 30: 1255-1268.

[2] Liew K.M., Xiang Y., Kitipornchai S., 1994, Transverse vibration of thick rectangular plates-IV: influence of isotropic in-plane pressure, Computers and Structures 49: 69-78.

[3] Liu F.L., Liew K.M., 1999, Analysis of vibrating thick rectangular plates with mixed boundary constraints using differential quadrature element method, Journal of Sound and Vibration 225: 915-934.

[4] Shen H.S., Yang J., Zhang L., 2000, Dynamic response of Reissner-Mindlin plates under thermomechanical loading and resting on elastic foundations, Journal of Sound and Vibration 232: 309-329.

[5] Li S.R., Zhou Y.H., Song X., 2002, Non-linear vibration and thermal buckling of an orthotropic annular plate with a centric rigid mass, Journal of Sound and Vibration 251: 141-152.

[6] Ebrahimi F., Rastgoo A., 2008, Free vibration analysis of smart annular FGM plates integrated with piezoelectric layers, Smart Materials and Structures, doi:10.1088/0964-1726/17/1/015044.

[7] Xuefeng S., Xiaoqing Z., Jinxiang Z., 2000, Thermoelastic free vibration of clamped circular plate, Applied Mathematics and Mechanics 21: 715-724.

[8] Arafat H.N., Nayfeh A.H., Faris W., 2004: Natural frequencies of heated annular and circular plates, International Journal of Solids and Structures 41: 3031-3051.

[9] 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, doi:10.1088/0964-1726/18/8/085015.

[10] Ebrahimi F., Rastgoo A., Atai A.A., 2008, A theoretical analysis of smart moderately thick shear deformable annular functionally graded plate, European Journal of Mechanics A/Solids, doi: 10.1016/j.euromechsol.2008.12.008.

[11] Praveen G.N., Reddy J.N., 1998, Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates, International Journal of Solids and Structures 35: 4457-4476.

[12] Reddy J.N., 2000, Analysis of functionally graded plates, International Journal of Numerical Methods in Engineering 47: 663-684.

[13] Woo J., Meguid S.A., 2001, Nonlinear analysis of functionally graded plates and shallow shells, International Journal of Solids and Structures 38: 7409-7421.

[14] Woo J., Meguid S.A., Ong L.S., 2006, Nonlinear free vibration behavior of functionally graded plates, Journal of Sound and Vibration 289: 595-611.

[15] Allahverdizadeh A., Naei M.H., Ratgo A., 2006, The effects of large vibration amplitudes on the stresses of thin circular functionally graded plates, International Journal of Mechanics and Materials in Design 3: 161-174.

[16] Kitipornchai S, Yang J., Liew K.M., 2004, Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections, International Journal of Solids and Structures 41: 2235-2257.

[17] Kitipornchai S., Yang J., Liew K.M., 2006, Random vibration of the functionally graded laminates in thermal environments, Computer Methods in Applied Mechanics and Engineering 195: 1075-1095.

[18] Shafiee H., Naei M.H., Eslami M.R., 2006, In-plane and out-of-plane buckling of arches made of FGM, International Journal of Mechanical Sciences 48: 907-915.

[19] Huang X.L., Shen H.S., 2004, Nonlinear vibration and dynamic response of functionally graded plates in thermal environments, International Journal of Solids and Structures 41: 2403-2427.

[20] Mindlin R.D., 1951, Influence of rotary inertia and shear on flexural motions of isotropic elastic plates, Journal of Applied Mechanics 18: 31-8.

[21] Reddy J.N., 1999, Theory and Analysis of Elastic Plates, Taylor and Francis, Philadelphia.

[22] Huang S., 1998, Non-linear vibration of a hinged orthotropic circular plate with a concentric rigid mass, Journal of Sound and Vibration 214: 873-883.

[23] Allahverdizadeh A., Naei M.H., Nikkhah Bahrami M., 2008, Nonlinear free and forced vibration analysis of thin circular functionally graded plates, Journal of Sound and Vibration 310: 966-984.

[24] Ma L.S., Wang T.J., 2003, Nonlinear bending and post-buckling of a functionally graded circular plate under mechanical and thermal loadings, International Journal of Solids and Structures 40: 3311-3330.

[25] Han J.B,, Liew K.M., 1999, Axisymmetric free vibration of thick annular plates, International Journal of Mechanical Sciences 41: 1089-1109.

[26] Haterbouch M.,, Benamar R., 2004, The effects of large vibration amplitudes on the axisymmetric mode shapes and natural frequencies of clamped thin isotropic circular plates, part II: iterative and explicit analytical solution for non-linear coupled transverse and in-plane vibrations, Journal of Sound and Vibration 277: 1-30.