半无限弹性空间中移动荷载动力响应的r频域-波数域比例边界有限元法分析

摘要

基于Fourier积分变换和虚功原理,形成了频域-波数域比例边界有限元法,分析了移动荷载作用下半空间域弹性空间动力响应.首先对半无限域弹性体的动力控制方程进行时间到频域,荷载移动方向的空间域到波数的Fourier积分变换,然后选择比例中心,利用虚功原理,在地铁隧道孔洞横截面环向上采用有限元法意义离散,建立了频域-波数域比例边界有限元方程,进而形成了一阶微分矩阵方程形式的半无限空间动力刚度.文中理论推导表明:利用文中方法分析半无限域中沿地铁隧道结构纵轴向的移动荷载动力响应问题,不仅可避免无穷边界计算处理误差,而且可极大减小计算分析量.计算结果表明:半无限弹性地基的振动响应随移动荷载速度增大而增大,尤其是当荷载速度增大到土体剪切波速后,振动波传播到土体表面引起土体振动显著增大,土体振动性增大,将会对土体及表面结构的安全性形成一定影响,另一方面土体的振动在沿地铁隧道纵轴向的衰减比竖向慢.%Based on Fourier integral transformation and virtual work principle,a numerical analysis of the scaled boundary finite-element method in frequency-wave domain for the dynamic response of the elastic half-space to a moving load is proposed in this paper.With the application of double Fourier integral transformation from the time to frequency and space to wave-numbers,the elastodynamical governing equations of the half-space in the frequency-wave domain are derived.A scaled trans-formation in coordinates is performed and the FE discretization is performed along the circumferential direction of the tunnel, and thus the formulation of the scaled boundary finite element method in the frequency-wave domain is derived by virtual work principle.Then,the elastodynamical stiffness is transformed into a system of linear first-order ordinary differential equations. According to the proceeding of the proposed method demonstrates high efficiency and accuracy in dealing with the dynamic response of the subway tunnel embedded in the elastic half-space subjected to a moving load.Numerical results are presented to show that the vibration response of the elastic half-space increases with the increase of the speed of the moving load,especially when the load speed gets close to the shear wave velocity.It also shows that the dynamic response of the surface of the half space increases dramatically with the vibration wave propagating to the soil surface,which increases the risk of structural damage to the tunnel or any overlying structure.Also,compared with the vertical vibration of the elastic half-space,the speed of the horizontal vibration attenuation along the longitudinal axis of the subway tunnel is slower.