移动荷载下弹性半空间地基上矩形薄板的动力响应解析研究  

Analytical study on dynamic response of rectangular thin plate on an elastic half-space under moving loads

作　　者：王春玲[1] 黄必成[1] 曹彩芹[1] 

机构地区：[1]西安建筑科技大学,陕西西安710055

出　　处：《土木工程学报》2016年第1期116-121,共6页China Civil Engineering Journal

基　　金：国家自然科学基金(51178387);陕西省自然科学基础研究计划项目(2014JM1033)

摘　　要：基于三维弹性理论,先对位移表示的地基动力方程进行Laplace变换,再进行双重傅里叶变换,获得直角坐标系下弹性半空间地基受任意竖向动荷载作用下的Laplace变换域中的位移解析表达式;然后对地基上有限大矩形薄板的边值问题进行Laplace变换,并求得地基板的Laplace变换域中的含有未知地基反力的挠度解析解;最后结合板与地基的变形协调方程,完全求得弹性半空间地基板在移动荷载作用下的Laplace变换域中的解析解。在此基础上,利用Laplace数值逆变换得到地基板时间域内的动力响应。算例结果表明本文的研究方法是切实可行的。用该文方法可精确分析地基板在任意移动载荷作用下的动力特性。Based on three-dimensional elasticity theory,the Laplace transform was firstly applied to the dynamic equations of ground represented by displacements,and then the Fourier transform was applied twice to obtain the analytical expression of displacement in Laplace transform domain for the elastic half-space under arbitrary dynamic loads in the rectangular coordinate system. Secondly,the Laplace transform was applied to the boundary value problem of the limited-size thin plate on the ground,so that the analytical solution of deflection expressed with ground reaction forces in the Laplace transform domain of plate can be achieved. Finally,in combination with the deformation compatibility equations of plate and ground,the analytical solution in the Laplace transform domain of plate on the elastic half-space under a moving load can be obtained. Furthermore,the dynamical responses in the time domain of the plate were obtained using the numerical inversion of Laplace transform. The example results show that the proposed method is practically feasible,and with the method proposed in this study,the dynamic characteristics of plate on the elastic halfspace under arbitrary moving loads can be accurately analyzed.

关 键 词：LAPLACE变换 傅里叶变换 弹性半空间地基 有限大矩形薄板 移动荷载 

分 类 号：TU31[建筑科学—结构工程]