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基于饱和多孔弹性Timoshenko梁的动力数学模型,研究了梁中点承受突加载荷作用两端可渗透饱和多孔弹性Timoshenko简支梁的动力响应,得到了问题的解析解,给出了梁中点无量纲挠度、固相骨架弯矩和孔隙流体压力等效力偶等随无量纲时间的响应。考察了剪切和横截面转动惯性效应等对动力响应的影响,比较了饱和多孔Timoshenko、Shear、Rayleigh和Euler-Bernoulli梁的动力响应,结果表明:剪切效应使饱和多孔Timoshenko梁动力响应的幅值和周期增大,而横截面转动惯性仅增加梁动力响应的周期;固相骨架与孔隙流体的相互作用具有粘性效应,随着相互作用系数的增加,饱和多孔梁挠度和弯矩幅值减小,流体压力等效力偶幅值增大,且振幅衰减加快。同时,随着长细比的增加,饱和多孔Timoshenko梁的挠度幅值和周期逐渐减小,并最终趋于饱和多孔Euler-Bernoulli梁的挠度幅值和周期。
Based on the dynamic mathematical model of saturated porous elastic Timoshenko beam, the dynamic response of Timoshenko simply supported beam with both ends permeable to sudden load is studied. The analytical solution of the problem is given. Synaptic deflection, solid skeleton moment and pore fluid pressure equal even with infinite dimension time response. The dynamic responses of saturated porous Timoshenko, Shear, Rayleigh and Euler-Bernoulli beams are investigated. The results show that the shearing effect makes the dynamic response of saturated porous Timoshenko beam amplitude The value and the period increase, but the rotational inertia of the cross section only increases the period of the dynamic response of the beam. The interaction between the solid skeleton and the pore fluid has a viscous effect. With the increase of the interaction coefficient, the deflection of the saturated porous beam and the amplitude of the bending moment decrease Small, fluid pressure equivalent force even amplitude increases, and amplitude attenuation accelerated. At the same time, as the slenderness ratio increases, the deflection amplitude and period of the saturated porous Timoshenko beam gradually decrease, and eventually reach the deflection amplitude and period of the saturated porous Euler-Bernoulli beam.