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首页> 外文期刊>Transport in Porous Media >Dynamic Response of a Multilayered Poroelastic Half-Space to Harmonic Surface Tractions
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Dynamic Response of a Multilayered Poroelastic Half-Space to Harmonic Surface Tractions

机译：多层多孔弹性半空间对表面谐波的动力响应

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摘要

The propagator matrix method is developed to study the dynamic response of a multilayered poroelastic half-space to time-harmonic surface tractions. In a cylindrical coordinate system, a method of displacement potentials is applied first to decouple the Biot’s wave equations into four scalar Helmholtz equations, and then, general solutions to those equations are obtained. After that, the propagator matrix method and the vector surface harmonics are employed to derive the solutions for a multilayered poroelastic half-space subjected to surface tractions. It is known that the original propagator algorithm has the loss-of-precision problem when the waves become evanescent. At present, an orthogonalization procedure is inserted into the matrix propagation loop to avoid the numerical difficulty of the original propagator algorithm. Finally, a high-order adaptive integration method with continued fraction expansions for accelerating the convergence of the truncated integral is adopted to numerically evaluate the integral solutions expressed in terms of semi-infinite Hankel-type integrals with respect to horizontal wavenumber. Furthermore, to validate the present approach, the response of a uniform poroelastic half-space is examined using the formulation proposed in this article. It is shown that the numerical results computed with this approach agree well with those computed with the analytical solution of a uniform half-space.
机译：发展了传播矩阵方法，以研究多层多孔弹性半空间对时谐表面牵引的动力响应。在圆柱坐标系中，首先应用位移势的方法将比奥的波动方程解耦为四个标量亥姆霍兹方程，然后获得这些方程的一般解。此后，采用传播矩阵法和矢量表面谐波的方法，得出了承受表面牵引力的多层多孔弹性半空间的解。众所周知，当波渐逝时，原始的传播器算法存在精度损失的问题。目前，将正交化程序插入矩阵传播环路中以避免原始传播算法的数值困难。最后，采用连续分数扩展的高阶自适应积分方法，以加速截断积分的收敛，对水平波数以半无限汉克尔积分表示的积分解进行数值评估。此外，为验证本方法，使用本文中提出的公式检查了均匀多孔弹性半空间的响应。结果表明，用这种方法计算出的数值结果与用均匀半空间的解析解计算出的数值结果非常吻合。

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