饱和地基上含刚核弹性圆板的摇摆振动分析

ROCKING VIBRATIONS OF A FLEXIBLE PLATE WITH RIGID CORE ON SATURATED GROUND

基于饱和土弹性波动方程,研究了饱和地基上含刚核弹性圆板在摇摆谐和力矩作用下的振动特性。首先应用Hankel积分变换求解该饱和土波动方程,然后按混合边值条件建立起一组描述含刚核弹性圆板振动的对偶积分方程,并将其化为第二类Fredholm积分方程进行数值求解。此外,给出了含刚核弹性圆板在饱和地基上振动的阻抗函数随无量纲频率的变化曲线,并考察了土的渗透系数、弹性板含刚域的大小以及板的柔度等参数对阻抗函数的影响,得出了一些有意义的结论。

The rocking vibration of a flexible circular plate with rigid core resting on saturated ground is studied. Based on the theory of elastic wave in saturated soil, the displacement solutions in Hankel transformed domain to the governing differential equations for saturated soil are obtained. With the assumption of adhesive contact between the plate and the ground surface, by keeping the rocking angle of the internal core constant and the flexible plate satisfying the equation of motion of a classic thin plate, dual integral equations which describe the mixed boundary-value problem for the plate are established. The equations are transformed to the second kind Fredholm integral equations. A numerical procedure is proposed to solve the equations. The dynamic impedance functions for rocking vibration are also derived. The effects of ground permeability, rigid core size and plate flexibility on the impedance functions are investigated and some meaningful conclusions are obtained.