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不可压饱和多孔Timoshenko梁动力响应的数学模型
引用本文:宋少沪,姚戈,杨骁.不可压饱和多孔Timoshenko梁动力响应的数学模型[J].固体力学学报,2010,31(4):397-405.
作者姓名:宋少沪  姚戈  杨骁
作者单位:1. 上海大学 土木工程系2. 上海大学
基金项目:国家自然科学基金项目 
摘    要:基于饱和多孔介质理论,假定孔隙流体仅沿梁的轴向运动,论文建立了横观各向同性饱和多孔弹性Timoshenko梁动力响应的一维数学模型,通过不同的简化,该模型可分别退化为饱和多孔梁的Euler-Bernoulli模型、Rayleigh模型和Shear模型等.研究了两端可渗透Timoshenko简支梁自由振动的固有频率、衰减率和阶梯载荷作用下的动力响应特征,给出了梁弯曲时挠度、弯矩以及孔隙流体压力等效力偶等随时间的响应曲线,并与饱和多孔弹性Euler-Bernoulli简支梁的响应进行了比较,考察了固相与流相相互作用系数、梁长细比等的影响.可见,固相骨架与孔隙流体的相互作用具有粘性效应,随着作用系数的增加,梁挠度振动幅值衰减加快,并最终趋于静态响应,Euler-Bernoulli梁的挠度幅值和振动周期小于Timoshenko梁的挠度幅值和周期,而Euler-Bernoulli梁的弯矩极限值等于Timoshenko梁的弯矩极限值.

关 键 词:饱和多孔介质理论  多孔Timoshenko梁  数学模型  动力响应  
收稿时间:2009-04-17

MATHEMATICAL MODEL FOR DYNAMICS OF INCOMPRESSIBLE SATURATED POROELASTIC TIMOSHENKO BEAM
Shaohu Song,Ge Yao,Xiao Yang.MATHEMATICAL MODEL FOR DYNAMICS OF INCOMPRESSIBLE SATURATED POROELASTIC TIMOSHENKO BEAM[J].Acta Mechnica Solida Sinica,2010,31(4):397-405.
Authors:Shaohu Song  Ge Yao  Xiao Yang
Abstract:Based on the theory of saturated porous media, a mathematical model for dynamics of the transversely isotropic saturated poroelastic Timoshenko beam is established with assumption that fluid in pores moves only in the axial direction of the beam. Under some limiting cases, this mathematical model can be degenerated into Euler-Bernoulli Model, Rayleigh Model and Shear Model of the poroelastic beam respectively. With the mathematical model presented, the natural frequencies and attenuations for free vibration and the dynamical behavior of the simply-supported poroelastic Timoshenko beam, with two ends permeable and subjected to the step load are investigated. The variations of the deflections, bending moments of the poroelastic beam and the equivalent couples of the pore fluid pressure are shown in figures and are compared with the results of the simply-supported poroelastic Euler-Bernoulli beam. The influences of the interaction coefficient between the solid skeleton and the slenderness ratio of the beam are discussed. It is shown that the interaction coefficient plays a role as viscidity. The amplitudes of deflection attenuate more rapidly with the increasing of the interaction coefficient, and the deflection approaches to that of the static response. Furthermore, the deflection amplitude and period of the poroelastic Euler-Bernoulli beam are smaller than those of the poroelastic Timoshenko beam, and the limit values of the bending moments are the same for the poroelastic Euler-Bernoulli beam and Timoshenko beam.
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