横观各向同性饱和地基上中厚圆板的非轴对称振动

Non-axisymmertrical Vibration of Elastic Thick Circular Plate on Transversely Isotropic Saturated Soil Ground

研究横观各向同性饱和土地基上中厚弹性圆板的非轴对称振动问题。基于横观各向同性饱和介质Biot波动方程的一般解,按混合边值问题建立了饱和地基与弹性中厚圆板非轴对称动力相互作用的对偶积分方程,并将对偶积分方程转化为易于计算的第二类Fredholm积分方程;采用数值方法求解该积分方程。数值算例结果表明,当h/a>0.05时,饱和半空间体上中厚度圆板在不同频率下的振动特性与相应频率下的刚性板的振动特性基本相同,当h/a<0.05时,板中心的位移将随h/a的减小而增大。

A pair of dual integral equations, which describe the mixed boundary-value problem for dynamic interaction between a half-space with transversely isotropic saturated soil and elastic thick circular plate, is established based on the general solutions of Biot's motion equations for transversely isotropic saturated poroelastic media Then the dual integral equations are reduced to the Fredholm integral equation of the second kind and numerically solved, which shows that the vibration features of elastic thick circular plate on saturated half-space excited by the different frequency are similar to that of rigid plate as h/d>0.05, whereas the displacement at centre of plate increases with the decreasing h/a.