层状横观各向同性饱和地基上圆板的非轴对称振动

Non-Axisymmetrical Vibration of Elastic Circular Plate on Layered Transversely Isotropic Saturated Ground

研究了层状横观各向同性饱和地基上弹性圆板的非轴对称振动问题.首先,通过方位角的Fourier变换,将圆柱坐标系下横观各向同性饱和土的三维动力方程转化为一阶常微分方程组,基于径向Hankel变换,建立问题的状态方程,求解状态方程后得到传递矩阵;其次,利用传递矩阵,结合层状饱和地基的边界条件、排水条件及层间接触和连续条件,给出了任意简谐激振力作用下层状横观各向同性饱和地基动力响应的通解;然后,按混合边值问题建立层状饱和地基上弹性圆板非轴对称振动的对偶积分方程,并将对偶积分方程化为易于数值计算的第二类Fredholm积分方程,并给出了算例.

The non-axisymmetrical vibration of elastic circular plate resting on a layered transversely isotropic saturated ground is studied. First, the 3-d dynamic equations in cylindrical coordinate for transversely isotropic saturated soil were transformed into a group of governing differential equations with l-order by the technique of Fourier expanding with respect to azimuth, and the state equation was established by Hankel integral transform method, furthermore the transfer matrixes within layered media were derived based on the solutions of the state equation. Secondly, by the transfer matrixes, the general solutions of dynamic response for layered transversely isotropic saturated ground excited by an arbitrary harmonic force were established under the boundary conditions, drainage conditions on the surface of ground as well as the contact conditions. Thirdly, the problem was led to a pair of dual integral equations describing the mixed boundary-value problem which can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure easily. At the end, a numerical result concerning vertical and radical displacements of both the surface of saturated ground and plate was evaluated.