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Dynamic response of an elastic plate on a transversely isotropic viscoelastic half-space with variable with depth moduli to a rectangular moving load
Soil Dynamics and Earthquake Engineering ( IF 4 ) Pub Date : 2020-12-01 , DOI: 10.1016/j.soildyn.2020.106330
Edmond V. Muho

Abstract The dynamic response of a flexural elastic plate on a transversely isotropic half-space with elastic constants varying with depth to a rectangular load moving with constant speed is determined analytically. Soil viscoelasticity via hysteric damping and plate viscous damping is also considered. Use is made of the method of the complex Fourier series involving the two horizontal coordinates and the time. Because the load speed is constant, only a double series expansion of the response functions is required. Employment of this method reduces the partial differential equations of motion for the soil and the plate to ordinary differential equations with variable coefficients and an algebraic equation, respectively. Those ordinary differential equations are solved by the method of Frobenius. Use of boundary conditions and equilibrium and compatibility at the soil-plate interface help to determine the constants of integration and obtain the soil and plate response in closed form. Verification of the obtained solution is done by using it to determine the response of simpler cases to moving loads for which there are analytical results in the existing literature. Parametric studies are finally conducted to assess the effects of viscoelasticity, cross-anisotropy and non-homogeneity of soil, of stiffness of the plate, as well as of load speed on the plate response.

中文翻译:

弹性板在随深度模量变化的横向各向同性粘弹性半空间上对矩形移动载荷的动态响应

摘要 分析确定了弹性常数随深度变化的横向各向同性半空间上的弯曲弹性板对等速矩形载荷的动态响应。还考虑了通过滞后阻尼和板粘性阻尼产生的土壤粘弹性。使用涉及两个水平坐标和时间的复傅立叶级数的方法。因为负载速度是恒定的,所以只需要对响应函数进行二次级数展开。采用这种方法将土和板的运动偏微分方程分别简化为具有可变系数的常微分方程和代数方程。这些常微分方程是用 Frobenius 方法求解的。在土板界面使用边界条件和平衡和相容性有助于确定积分常数并获得封闭形式的土板响应。所获得的解决方案的验证是通过使用它来确定更简单的情况下对移动载荷的响应,现有文献中有分析结果。最后进行参数研究以评估土壤的粘弹性、交叉各向异性和非均匀性、板刚度以及加载速度对板响应的影响。所获得的解决方案的验证是通过使用它来确定更简单的情况下对移动载荷的响应,现有文献中有分析结果。最后进行参数研究以评估土壤的粘弹性、交叉各向异性和非均匀性、板刚度以及加载速度对板响应的影响。所获得的解决方案的验证是通过使用它来确定更简单的情况下对移动载荷的响应,现有文献中有分析结果。最后进行参数研究以评估土壤的粘弹性、交叉各向异性和非均匀性、板刚度以及加载速度对板响应的影响。
更新日期:2020-12-01
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