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首页> 外文期刊>Applied Mathematical Modelling >Time-harmonic response of transversely isotropic and layered poroelastic half-spaces under general buried loads
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Time-harmonic response of transversely isotropic and layered poroelastic half-spaces under general buried loads

机译：一般掩埋荷载下横观各向同性和层状多孔弹性半空间的时谐响应

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摘要

A semi-analytical method is developed for solving the dynamic response of transversely isotropic, multilayered, and poroelastic half-spaces with different surface hydraulic conditions and subjected to time-harmonic vertical and horizontal loads buried in the layered half-space. The coupled governing equations of motion are presented in details in terms of the Biot's poroelastodynamic theory via the (u,p) formulation. The cylindrical system of vector functions is introduced to express the unknown primary quantities so that the coupled governing partial differential equations can be reduced and separated into two sets of first-order ordinary differential equations (i.e., the LM- and N-types). A recursive relation for the expansion coefficients among different layers is established by virtue of the stable and efficient dual variable and position method. Making use of the boundary and interface conditions, the fundamental solutions are obtained in terms of the vector-function system. The corresponding physical-domain solutions are then derived via an accurate semi-infinite integral algorithm. The developed fundamental solutions are carefully checked with existing solutions, and numerical examples are further presented to demonstrate the effect of material anisotropy, loading depth, material layering, and surface hydraulic condition on the dynamic response, which should be useful to design engineers. These solutions could be further served as benchmarks for future numerical methods.
机译：开发了一种半解析方法，用于求解具有不同表面水力条件的横向各向同性的，多层的和多孔弹性的半空间的动力响应，并承受埋藏在分层半空间中的时谐垂直和水平载荷。通过（u，p）公式，根据毕奥的孔隙弹性理论，详细介绍了耦合的运动控制方程。引入了向量函数的圆柱系统来表达未知的一次量，从而可以简化耦合的控制偏微分方程并将其分成两组一阶常微分方程（即LM型和N型）。借助稳定高效的对偶变量和位置方法，建立了不同层之间膨胀系数的递归关系。利用边界和界面条件，根据矢量函数系统获得了基本解。然后，通过精确的半无限积分算法得出相应的物理域解。所开发的基本解决方案已与现有解决方案进行了仔细检查，并通过数值示例进一步说明了材料各向异性，加载深度，材料分层和表面水力条件对动力响应的影响，这对设计工程师应该是有用的。这些解决方案可以进一步用作未来数值方法的基准。

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