非线性弹性地基上矩形薄板的动力学研究

摘要

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；导出频率响应方程,研究了频率响应特性；讨论非线性因素的影响,得出了忽略地基板非线性因素的条件；分析地基板的非线性振动稳定性,得出了稳定区和不稳定区的分界线方程.%The seismic response characteristics and vibration stability of a thin rectangular plate on nonlinear elastic foundation were investigated in consideration of the damping and the nonlinear effect of the foundation plate.A nonlinear dynamical equation of the small deformation thin rectangular plate on nonlinear elastic foundation subjected to harmonic excitation was established.The frequency response equation was derived,the frequency response characteristics were solved and nonlinear dynamic responses to a seismic excitation were analyzed by using the method of harmonic balance.The effects of nonlinear factors and the nonlinear vibration stability of the foundation plate were studied.The boundary equation dividing steady region and instable region was obtained.The condition,under which nonlinear factors of the foundation plate can be ignored,was acquired.The conclusions are helpful to the accurate design and effect analysis of the foundation plate.