含液饱和多孔二维梁的动力特性分析

DYNAMIC RESPONSE ANALYSIS OF A TWO DIMENSIONAL FLUID-SATURATED POROUS BEAM

基于线弹性理论和Biot多孔介质模型,分析了含液饱和多孔二维简支梁的动力响应,其中考虑了固体颗粒和流体的可压缩性以及孔隙流体的粘滞性。通过Fourier级数展开和常微分方程组的求解,得到了含液饱和多孔二维梁动力响应问题的解,并将其退化为单相固体二维梁的情形与Bernoulli-Euler梁和Timoshenko梁的自由振动相比较,验证了该文方法的正确性。作为数值算例,分析了含液饱和多孔二维梁的自由振动以及在均布简谐荷载作用下的动力响应特性,分析了表面渗透条件、孔隙流体渗透系数和荷载频率等参数对含液饱和多孔二维梁的自由振动频率、固相位移和孔隙流体压力等物理量的影响。

Based on linear elastic theory and Biot's theory for saturated porous media, the dynamic response of a two dimensional fluid-saturated porous beam is studied, in which the compressibility of solid particles and fluid and the viscosity of the pore fluid are taken into account. Using Fourier series expansion and solving the ordinary differential equations, a solution for the dynamic response of the two dimensional simply-supported fluid-saturated porous beam is obtained. By degenerating the beam into a single-phase two-dimensional solid beam, the presented methodology is validated by comparing the free vibration frequency of the beam with that of a Bernoulli-Euler beam and a Timoshenko beam. As a numerical example, the dynamic response characteristics of the free vibration and forced vibration of the beam under uniformly distributed harmonic load are analyzed. The influences of surface infiltration condition, pore fluid permeability coefficient, and loading frequency parameters, etc. on the free vibration, solid displacement and pore fluid pressure of the two-dimensional fluid-saturated porous beam are studied.