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集中载荷作用下饱和多孔Timoshenko简支梁的动力响应
引用本文:欧阳煜, 张雅男. 集中载荷作用下饱和多孔Timoshenko简支梁的动力响应[J]. 工程力学, 2012, 29(11): 325-331. DOI: 10.6052/j.issn.1000-4750.2011.01.0058
作者姓名:欧阳煜  张雅男
作者单位:(上海大学土木工程系,上海 200072)
基金项目:国家自然科学基金项目(10872124)
摘    要: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。

关 键 词:饱和多孔Timoshenko梁  数学模型  动力响应  剪切效应  惯性效应
收稿时间:2011-01-21
修稿时间:2011-04-20

DYNAMICAL BEHAVIOR OF SIMPLY-SUPPORTED SATURATED POROELASTIC TIMOSHENKO BEAM UNDER A CONCENTRATED LOAD
OUYANG Yu, ZHANG Ya-nan. DYNAMICAL BEHAVIOR OF SIMPLY-SUPPORTED SATURATED POROELASTIC TIMOSHENKO BEAM UNDER A CONCENTRATED LOAD[J]. Engineering Mechanics, 2012, 29(11): 325-331. DOI: 10.6052/j.issn.1000-4750.2011.01.0058
Authors:OUYANG Yu  ZHANG Ya-nan
Affiliation:(Department of Civil Engineering, Shanghai University, Shanghai 200072, China)
Abstract:Based on the mathematical model for dynamics of a saturated poroelastic Timoshenko beam,the dynamical behavior of a simply-supported saturated poroelastic Timoshenko beam,with two permeable ends and subjected to a sudden step load at its midpoint,is investigated.The analytical solution is obtained,and the variations of the dimensionless deflections,bending moments of the solid skeleton of the poroelastic beam,and equivalent couples of the pore fluid pressure against the dimensionless time are given.The effects of the shearing and rotation inertia of the cross section on the dynamical behavior are examined,and the dynamical behaviors of the saturated poroelastic Timoshenko,Shear,Rayleigh and Euler-Bernoulli beams are compared.It is shown that the shearing effect increases the amplitudes and periods of the dynamical responses of the saturated poroelastic Timoshenko beam,while the rotation inertia effect of the cross section only increases the periods.The interaction between the solid skeleton and pore fluid plays a role as viscidity.With the interaction coefficient increasing,the deflections and bending moments of the saturated poroelastic beam decrease,and the amplitudes of the equivalent couple of the pore fluid pressure increase,furthermore,the attenuation of the vibration amplitudes is more rapidly with the increasing of the interaction coefficient.Meanwhile,with the slenderness ratio increasing,the amplitude and period of the saturated poroelastic Timoshenko beam decrease gradually,and they converge to those of the saturated poroelastic Euler-Bernoulli beam.
Keywords:saturated poroelastic Timoshenko beam  mathematical model  dynamical behavior  shearing effect  inertia effect
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