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利用半解析的方法研究了饱和地基表面刚性圆形基础在倾斜入射SH波作用下的扭转振动问题。假设基础以下为Biot波动方程描述的饱和半空间,通过Hankel变换把Biot波动方程转化为常微分方程进行求解。将土体中的波场划分为自由波场、刚体散射波场及辐射散射波场三部分。根据土体中波场的划分,结合基础与饱和半空间接触面的混合边值条件,建立两组描述刚性圆形基础扭转振动的对偶积分方程并用Nobel变换方法将其化为第二类Fredholm积分方程。通过求解Fredholm积分方程并结合基础刚体动力平衡方程,求得了基础在SH波作用下的扭转振动表达式。最终通过数值算例分析了波动频率、入射角度,基础扭转惯性矩以及饱和土体参数等对基础扭转振动的影响。
The semi-analytical method is used to study the torsional vibration of a rigid circular foundation on a saturated foundation under oblique incident SH wave. The following assumption is made on the basis of the saturated half-space described by Biot’s wave equation. The Biot’s wave equation is transformed into an ordinary differential equation by the Hankel transform. The wave field in soil is divided into three parts: free wave field, rigid body scattering wave field and radiation scattering wave field. According to the wave field in the soil, two sets of dual integral equations describing the torsional vibration of rigid circular foundation are established based on the mixed boundary conditions of the contact surface between the foundation and the saturated half-space and transformed into the second type of Fredholm integral by Nobel transformation equation. By solving the Fredholm integral equation and combining with the basic rigid body dynamic balance equation, the torsional vibrational expression of the foundation under the action of SH wave is obtained. Finally, numerical examples are given to analyze the influence of wave frequency, incident angle, moment of inertia of foundation and saturated soil parameters on torsional vibration of foundation.