非线性弹性地基上矩形薄板的动力学研究

本文研究了非线性弹性地基上矩形薄板的非线性振动特性和振动稳定性。在考虑了地基板阻尼和非线性效应的基础上，建立了小挠度矩形板横向均布简谐激励作用下的非线性动力学方程；用谐波平衡法研究了其非线性振动特性；导出了频率响应方程，研究了频率响应特性；讨论了非线性因素的影响，得出了忽略地基板非线性因素的条件；分析了地基板的非线性振动的稳定性，得出了稳定区和不稳定区的分界线方程。

RESEARCH ON DYNAMICS OF A THIN RECTANGULAR PLATE ON NONLINEAR ELASTIC FOUNDATION

Seismic response characteristics and vibration stability of the thin rectangular plate on nonlinear elastic foundation by damping of the foundation plate and nonlinear effect were investigated herein. A nonlinear dynamical equation of the small deformation thin rectangular plates on nonlinear elastic foundation subjected to harmonic excitation was established. The frequency response equation was derived and the frequency response characteristics was researched and nonlinear dynamic response to a seismic excitation were analyzed by the method of harmonic balance. The effectness of nonlinear factors and nonlinear vibration stability of the foundation plate were studied. The boundary equation of steady region and instability region was obtained. The condition of ignore nonlinear factors on the foundation plate was acquired. The conclusions of the paper are helpful to the accurate design and effect analysis of. the foundation plate.