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.
Based on the theory of saturated porous media,a one-dimensional mathematical model for dynamics of the transversely isotropic saturated poroelastic Timoshenko beam is established with assumption of the movement of the pore fluid 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 saturated poroelastic Timoshenko beam with two ends permeable and subject 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 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 deflections approaches to those 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.
出处
《固体力学学报》
CAS
CSCD
北大核心
2010年第4期397-405,共9页
Chinese Journal of Solid Mechanics
基金
国家自然科学基金项目(10872124)资助
