Abstract
Variations of stresses of a thin circular functionally grade plate, due to large vibration amplitudes, are developed in this paper. The plate thickness is constant and temperature dependent functionally graded material (FGM) properties vary through the thickness of the plate. For harmonic vibrations, governing equations are solved. Corresponding results are illustrated in the case of steady-state free vibration. The results show that the variation of volume fraction index is considerable in FGM properties and the amount of stresses.
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Brush, D.O., Almroth, B.O.: Buckling of Bars, Plates and Shells. McGraw-Hill, New York (1975)
Chen, C.-S.: Nonlinear vibration of a shear deformable functionally graded plate. Compos. Struct. 68, 295–302 (2005)
Dumir, P.C., Kumar, C.R., Gandhi, M.L.: Non-linear axisymmetric vibration of orthotropic thin circular plates on elastic foundations. J. Sound Vibration 103, 273–285 (1985)
Haterbouch, M., Benamar, R.: The effects of large vibration amplitudes on the axisymmetric mode shapes and natural frequencies of clamped thin isotropic circular plates. Part I: iterative and explicit analytical solution for non-linear transverse vibrations. J. Sound Vibration 265, 123–154 (2003)
Haterbouch, M., Benamar, R.: 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. J. Sound Vibration 277, 1–30 (2004)
Huang, C.L.D., Al-Khattat, I.M.: Finite amplitude vibrations of a circular plate. Int. J. Nonlinear Mech. 12, 297–306 (1977)
Huang, C.L., Sandman, B.E.: Large amplitude vibrations of rigidly clamped circular plates. Int. J. Nonlinear Mech. 6, 451–468 (1971)
Li, S.-R., Zhou, Y.-H.: Shooting method for non-linear vibration and buckling of heated orthotropic circular plates. J. Sound Vibration 248, 379–386 (2001)
Li, S.-R., Zhou, Y.-H.: Nonlinear vibration of heated orthotropic annular plates with immovably hinged edges. J. Thermal Stresses 26, 691–700 (2003)
Li, S.-R., Zhou, Y.-H., Song, X.: Nonlinear vibration and thermal buckling of an orthotropic annular plate with a centric rigid mass. J. Sound Vibration 251, 141–152 (2002)
Najafizadeh, M.M., Eslami, M.R.: Buckling analysis of circular plates of functionally graded materials under uniform radial compression. Int. J. Mech. Sci. 44, 2479–2493 (2002)
Praveen, G.N., Reddy, J.N.: Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates. Int. J. Solids Struct. 35(33), 4457–4476 (1998)
Reddy, J.N.: Analysis of functionally graded plates. Int. J. Numer. Meth. Eng. 47, 663–684 (2000)
Reddy, J.N., Cheng, Z.Q.: Frequency of functionally graded plates with three-dimensional asymptotic approach. J. Eng. Mech. 129, 896–900 (2003)
Reddy, J.N., Chin, C.D.: Thermo-mechanical analysis of functionally graded cylinders and plates. J. Thermal Stresses 21, 593–626 (1998)
Selmane, A., Lakis, A.A.: Natural frequencies of transverse vibrations of non-uniform circular and annular plates. J. Sound Vibration 220(2), 225–249 (1999)
Shafiee, H., Naei, M.H., Eslami, M.R.: In-plane and out-of-plane buckling of arches made of FGM. Int. J. Mech. Sci. 48, 907–915 (2006)
Timoshenko, S., Woinowsky-Krieger, S.: Theory of Plates and Shells, 2nd edn. McGraw-Hill, New York (1959)
Touloukian, Y.S.: Thermo Physical Properties of high Temperature Solid Materials. Macmillan, New York (1967)
Woo, J., Meguid, S.A.: Nonlinear analysis of functionally graded plates and shallow shells. Int. J. Solids Struct. 38, 7409–7421 (2001)
Yang, J., Shen, H.S.: Dynamic response of initially stressed functionally graded rectangular thin plates. Compos. Struct. 54, 497–508 (2001)
Yang, J., Shen, H.S.: Vibration characteristics and transient response of shear-deformable functionally graded plates in thermal environments. J. Sound Vibration 255, 579–602 (2002)
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Allahverdizadeh, A., Naei, M.H. & Rastgo, A. The effects of large vibration amplitudes on the stresses of thin circular functionally graded plates. Int J Mech Mater Des 3, 161–174 (2006). https://doi.org/10.1007/s10999-007-9020-8
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DOI: https://doi.org/10.1007/s10999-007-9020-8