This paper is concerned with the recent developments in the nonlinear vibrational analysis of plates of various geometries. Although most of the material presented here deals with geometric type nonlinearities, attention is also given to other types of nonlinearities such as nonlinear material behavior. Particular attention is given to the recent developments in the analytical methods of solution. Recent research leading to advances in numerical techniques is also included. Complicating effects such as the effects transverse shear deformation, rotatory inertia, anisotropy, initial imperfections, and variable rigidity on the vibration behavior of plates are reviewed and discussed. Finally, some general conclusions are presented along with the author’s views regarding the future research trends in this area.

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This paper comprises a survey on the nonlinear vibration analysis of plates, with emphasis on research carried out since 1987. Most of the research reviewed here deals with the effects of geometric nonlinearity on the vibration behavior of plates. Complicating factors such as material nonlinearity, geometric imperfections, transverse shear and rotatory inertia effects, and magnetic fields on the vibration behavior are included. Recent developments in the analytical and numerical methods of solution of isotropic, orthotropic as well as laminated, composite plates are presented. Experimental, analytical, and numerical investigations are included for all the cases reviewed and some general remarks are presented along with suggestions for future research directions.

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