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中文摘要：
基于Biot饱和多孔介质理论,以一类边界条件为例,提出一种单层饱和多孔介质一维瞬态响应问题的半解析求解方法。首先将基本方程和相应的初始条件、边界条件量纲一化,给出矩阵形式的位移控制方程。通过适当变换使边界条件齐次化,求解相应特征值问题,得到非齐次边界条件下的特征值和特征函数,并证明特征函数的正交性。利用该正交性,得到无限个仅阻尼项耦合的关于时间的常微分方程及相应的初始条件。截取有限项,采用精细时程积分法求解常微分方程组初值问题,并得到原问题的解,最后通过算例分析动力渗透系数对流固耦合作用的影响,验证方法的有效性。提出的方法不仅考虑孔隙流体、固体颗粒的压缩性及任意的惯性、黏滞和耦合作用,而且可以推广到任意非齐次边界条件的一维瞬态响应问题。
英文摘要：
Based on Biot theory,a semi-analytical approach is proposed to analyze the transient response of one-dimensional porous media;and the first typical boundary condition is adopted as an example.The dimensionless displacement governing equations with its initial and boundary conditions in matrix form are derived.A proper transform is applied to homogenizing the boundary condition;and the corresponding characteristic problem for the governing equations with viscous coupling omitted is solved to get a series of eigenvalues and characteristic functions,which are proved to be orthogonal.Using the orthogonality of characteristic functions,a series of ordinary differential equations and their initial conditions are derived.The ordinary differential equation system is only coupled in damping matrix and is solved by precise time-integration method when it is truncated as a finite ordinary differential equation system.Some examples are presented to demonstrate the influence of the dynamic permeability coefficient on propagation of waves.The method is valid for arbitrary non-homogeneous boundary conditions and suitable for problems considering inertia,viscous and mechanical couplings;and no limitation of compressibility of fluid and solid particles is required.
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