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工程力学  2012 

集中载荷作用下饱和多孔Timoshenko简支梁的动力响应

DOI: 10.6052/j.issn.1000-4750.2011.01.0058, PP. 325-331

Keywords: 饱和多孔Timoshenko梁,数学模型,动力响应,剪切效应,惯性效应

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Abstract:

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。

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