点弹性支承粘弹性矩形薄板的基频分析计算

NUMERICAL CALCULATION OF FUNDAMENTAL FREQUENCY OF VISCOELASTIC THIN RECTANGULAR PLATE WITH ELASTIC POINT SUPPORTS

从三维粘弹性本构关系出发,导出了具有多个点弹性支承的Kelvin型粘弹性矩形薄板的运动微分方程。针对方程中出现的二维广义d函数,采用积分方程法导出了具有多个点弹性支承的四边简支Kelvin型粘弹性矩形薄板自由振动的复特征方程,分析了材料的无量纲延滞时间、点弹性支承的弹性系数和支承位置对矩形薄板的固有频率的影响。

Based on the three-dimensional viscoelastic constitutive relationship, a differential equation of motion for Kelvin's viscoelastic thin rectangular plate with interior elastic point supports is derived, in which a two-dimensional generalized function δ appears. The complex characteristic equation for free vibration of Kelvin's viscoelastic thin rectangular plate with simple supports along all edges and additional interior point supports is obtained by the integral equation method. The effects of the dimensionless delay time of Kelvin's viscoelastic materials, the elastic constant of the elastic point supports and the location of the elastic point supports at the natural frequencies of the plate are discussed.