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考虑地基为饱和的且下卧基岩,研究了广义Gibson地基上刚性圆板在简谐扭转荷载作用下的动力响应问题。从饱和地基Biot理论出发,建立了剪切模量随深度线性变化的饱和地基动力微分方程,结合扭转振动的特点,通过Hankel变换求解了此微分方程,给出了Hankel变换域内的剪应力和切向位移。然后根据饱和地基与基础接触面处为混合边界条件、饱和地基与基岩接触面处应力和位移连续等边界条件,建立了描述扭转振动的对偶积分方程,借助数学方法求解此对偶积分方程,并给出了基础的动力柔度系数和角位移幅值的表达式。最后通过数值算例研究了地基的非均质性和渗透性对基础扭转特性的影响。
Considering the saturated and underlying bedrock, the dynamic response of a rigid circular plate on a generalized Gibson foundation under simple harmonic torsional loads is studied. Based on the Biot theory of saturated ground, a dynamic differential equation of saturated soil whose shear modulus changes linearly with depth is established. According to the characteristics of torsional vibration, this differential equation is solved by Hankel transform, and the shear stress and shear in Hankel transform are given To the displacement. Then based on the mixed boundary conditions of saturated foundation and foundation, the dual integral equations describing the torsional vibration are established by the boundary condition of continuous stress and displacement at the interface between saturated foundation and bedrock, and the dual integral equation is solved by mathematical method. The expressions of dynamic compliance coefficient and angular displacement amplitude are given. Finally, numerical examples are given to study the influence of the foundation’s anisotropy and permeability on the torsional behavior of foundation.