Nonlinear Vibration Analysis of Plates: A Review and Survey of Current Developments

Abstract

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.

Geometrically Non-Linear Free Vibration of Fully Clamped Symmetrically Laminated Rectangular Composite Plates

“…In the excellent monograph of Leissa [18], complemented by the journal paper [19], a summary of the knowledge and information on linear dynamic isotropic plate problems has been presented. Some references have also been given which are concerned with the large vibration amplitude problem, and have been considered as a good introduction to geometric type one-linearity [20]. Whitney and Leissa [21] have formulated the governing equations for non-linear vibrations of anisotropic plates based on the von KaH rmaH n theory.…”

“…In reference [28], a survey was presented of the literature on the geometric non-linear analysis of laminated composite elastic plates. Sathyamoorthy [20] has presented a review which deals with analytical, numerical and experimental methods used in the geometrically non-linear dynamic analysis of plates. A comprehensive survey of the "nite element method applied to non-linear vibration has been also presented.…”

Experimental and Theoretical Investigation of the Linear and Non-Linear Dynamic Behaviour of a Glare 3 Hybrid Composite Panel

“…These functions which satisfy all the fully clamped theoretical boundary conditions, i.e., zero displacement and zero slope along the four plate edges, have been used in previous studies on fully clamped rectangular plate vibration [10] and have been demonstrated in many cases to be appropriate for the determination of plate natural frequencies and mode shapes [13].…”

Non-Linear Vibration Characteristics of Clamped Laminated Shallow Shells

“…Chia [1,2] and Sathyamoorthy [3] collected and reviewed the comprehensive literature dealing with non-linear vibrations of laminated plates. Hui [4] investigated non-linear free vibrations of antisymmetrically laminated plates with geometric imperfections by using Lindstedt's perturbation method.…”