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考虑到地基在竖直方向上的非均匀性,结合扭转振动的特点,建立了简谐扭转动荷载作用时剪切模量随深度增大的广义Gibson饱和地基的动力方程,通过积分变换求解了动力方程。考虑到半空间地基表面处应力自由、埋置圆板所在平面为混合边界和无穷深度处为波的辐射边界等条件,得到了广义Gibson饱和地基中刚性圆板扭转振动时的对偶积分方程,通过合适的变换转化成了一个第2类Fredholm积分方程,求解了相应的动力响应问题。对比静扭距作用时的荷载-位移关系,给出了动力柔度系数和扭转角位移幅值的表达式,并把所研究的问题进行退化且与前人成果进行了对比。数值研究表明:当基础的埋置深度小于5倍基础半径时,广义Gibson饱和地基中埋置基础的扭转振动存在明显的边界层现象,且埋置深度越小,边界层现象越明显。
Considering the vertical inhomogeneity of foundation and the characteristics of torsional vibration, the dynamic equation of generalized Gibson saturated soil with shear modulus increasing with depth under simple torsional torsional load is established. The integral transformation is used to solve the dynamic equation Dynamic equation. The dual integral equations of torsional vibration of a rigid circular plate in a generalized Gibson saturated soil are obtained by considering the free stress at the surface of the semi-space foundation, the plane where the embedded circular plate is mixed and the radiation boundary at infinite depth. The appropriate transformation is transformed into a Fredholm integral equation of type 2, solving the corresponding dynamic response problem. Compared with the load-displacement relationship of static torque, the expression of dynamic flexibility coefficient and torsional angle displacement amplitude is given, and the problem under study is degenerated and compared with previous achievements. Numerical results show that there is a clear boundary layer phenomenon in the torsional vibration of the buried foundation in the generalized Gibson saturated soil when the foundation depth is less than 5 times the base radius. The more the embedment depth is, the more obvious the boundary layer phenomenon is.