Non-linear forced vibration analysis of rectangular plates including the coupling between transverse and in-plane displacements.

E Merrimi,R Benamar,K El Bikri

doi:10.1051/matecconf/20120110014

Abstract

The objective of this work is to study the geometrically non-linear steady state periodic forced response of fully clamped rectangular plates (FCRP) with immovable in-plane conditions, taking into account the effect of the in-plane displacements. A complete formulation has been proposed first, reducing the equations of motion to a system of coupled non-linear algebraic equations, which are decoupled once the in-plane inertia is omitted. An averaging technique has then been developed, in order to simplify the first method and to develop an engineering complete theory. The forced response is given in the case of a concentrated harmonic excitation force with various intensities. The numerical results obtained here with the two formulations, using an explicit analytical solution, were compared with those obtained previously using a formulation in which the in-plane displacements have been neglected, showing an “over-stiff” effect.

Highlights

Some problems of plate vibrations cannot be adequately analysed using the linear theory of vibration, which is based on the assumption that the middle plane of the plate is inextensible and that the vibration amplitude is small, compared to the plate thickness
The objective of this work is to study the geometrically non-linear steady state periodic forced response of fully clamped rectangular plates (FCRP) with immovable in-plane conditions, taking into account the effect of the in-plane displacements
The design of structural elements, especially plates undergoing large vibration amplitudes due to high excitation forces, arising in modern aircraft and naval constructions, requires determination of accurate estimates, or at least estimates which are good enough from the safety point of view, of the dynamic characteristics, which are useful for predicting the dynamic responses in the real operational environment

Summary

Introduction

Some problems of plate vibrations cannot be adequately analysed using the linear theory of vibration, which is based on the assumption that the middle plane of the plate is inextensible and that the vibration amplitude is small, compared to the plate thickness. Non-linear vibrations of plates have been analysed by numerous researchers using analytical, numerical, or combined approximate methods [1,2,3]. In a previous series of papers, a semi-analytical model for geometrically non-linear free and forced vibrations of elastic thin straight structures, such as beams, homogeneous and symmetrically laminated rectangular plates has been developed by Benamar et al [4]. The model was based on Hamilton’s principle and spectral analysis, and was of the same spirit as the well-known Rayleigh-Ritz method, used for numerical approximate solution of linear problems of vibration.

Objectives

Methods

Conclusion