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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 the linear elasticity theory and the Biot porous media model, the dynamic response of a two-dimensional fluid-saturated porous two-dimensional beam is analyzed, in which the compressibility of solid particles and fluid and the viscosity of pore fluid are considered. By solving Fourier series expansion and ordinary differential equations, the solution to the dynamic response of a two-dimensional beam with liquid-saturated porous material is obtained, which is degraded to a single-phase solid two-dimensional beam with a Bernoulli-Euler beam and a Timoshenko beam Free vibration compared to verify the correctness of the method. As numerical examples, the free vibration of liquid-filled porous two-dimensional beam and the dynamic response under uniform harmonic load are analyzed. The effects of surface permeation conditions, pore fluid permeability coefficient and load frequency on the stability of liquid-saturated Free two-dimensional beam frequency of free vibration, solid phase displacement and pore fluid pressure and other physical quantities.