The dynamic response of an elastic thin plate resting on a cross-anisotropic elastic half-space to a rectangular load moving on its surface with constant speed is analytically obtained. The moving load and the plate and soil displacements are expanded in double complex Fourier series involving the two horizontal coordinates x and y as well as the time and the load velocity. Thus, the plate equation of lateral motion reduces to an algebraic equation, while the soil equations of motion reduce to a system of three ordinary differential equations with respect to the vertical coordinate z, which can be easily solved. Compatibility and equilibrium at the plate–soil interface as well as employment of the boundary conditions of the system enable one to determine the solution in terms of displacements of the plate and the half-space soil medium. The solution is first verified by using it to obtain as special cases the solutions for isotropic and cross-anisotropic half-space problems and compare them against existing analytical solutions. Parametric studies are conducted to assess the effects of the degree of cross-anisotropy on the plate and soil responses in conjunction with the effects of other important parameters, such as the speed of the moving load.

中文翻译：

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矩形移动荷载作用下交叉各向异性弹性半空间上弹性板的动力学分析

解析地获得了位于交叉各向异性弹性半空间上的弹性薄板对在其表面上匀速移动的矩形载荷的动态响应。移动荷载和板和土位移在双复傅立叶级数中展开，涉及两个水平坐标 x 和 y 以及时间和荷载速度。这样，横向运动的平板方程简化为代数方程，而土壤运动方程简化为三个关于垂直坐标z的常微分方程组，易于求解。板 - 土界面的相容性和平衡以及系统边界条件的使用使人们能够根据板和半空间土壤介质的位移来确定解决方案。该解首先通过使用它来获得作为特殊情况的各向同性和交叉各向异性半空间问题的解并将它们与现有解析解进行比较来验证。进行参数研究以评估交叉各向异性程度对板和土壤响应的影响以及其他重要参数的影响，例如移动载荷的速度。