SH波作用下饱和地基表面刚性圆形基础扭转振动分析

Torsional vibration of a rigid circular foundation resting on poroelastic half-space subjected to obliquely incident SH waves

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。

A semi-analytical approach is used to study the torsional vibration of a rigid circular foundation resting on poroelastic half-space subjected to obliquely incident SH waves.The Biot＇s dynamic poroelastic theory is employed to characterize the saturated half-space.The governing equations for the saturated half-space and foundation are solved by using the Hankel transform.The total wave field in the saturated half-space is classified into free-field waves,rigid-body scattering waves and radiation scattering waves.According to the classification of the total wave field and the mixed boundary-value condition between the saturated half-space and foundation,the torsional vibration of the foundation is formulated into two sets of dual integral equations.Then,the integral equations are reduced to Fredholm integral equations of the second kind to solve.Considering the dynamic equilibrium equation of the foundation,the torsional vibration expression of the foundation is obtained.Numerical results are presented to demonstrate the effects of wave frequency,incident angle of the waves,the torsional inertia moment of the foundation and permeability of the saturated half-space on the torsional vibration.