下卧基岩横观各向同性饱和地基上刚性圆板的扭转振动

通过Hankel变换求解了横观各向同性饱和地基在简谐扭矩作用下的动力方程，结合基础与地基接触面为混合边界和基岩面处地基位移为零的边界条件，建立了刚性基础的扭转对偶积分方程，化对偶积分方程为第二类Fredholm积分方程求解了相应的动力响应问题，并给出了基础的动力柔度系数和角位移幅值以及基底接触剪应力的表达式.数值分析结果表明：下卧基岩饱和地基上基础扭转动力柔度系数的实部和虚部都呈现出一定的波动，地基的各向异性程度对基础的动力柔度系数和扭转角位移幅值有很大影响；基础的振动频率和地基的各向异性程度对基底接触剪应力的分布也有一定影响.

Torsional vibrations of rigid disk resting on transversely isotropic saturated soil overlaying bedrock

The dynamic differential equations of transversely isotropic saturated soil subjected to harmonic torque were solved by using the Hankel transform.Combining the mixed boundary conditions at the interface between the foundation and the saturated soil and the fixed boundary condition at the surface of the bedrock,the torsional dual integral equations of the rigid foundation were established,and further converted to Fredholm integral equations of the second kind.The dynamic interaction problem was solved by solving the integral equation.Numerical results indicate that both the real part and the imaginary part of the dynamic compliance coefficients of the foundation show obvious fluctuation,and that the saturated soil's anisotropy has significant effect on the dynamic compliance coefficients and the angular amplitude of the foundation.Furthermore,the distribution of the contact shear stress under the foundation is affected by the vibration frequency and the anisotropy of the saturated soil.