含液饱和不可压多孔弹性板的随机振动

摘要

On the basis of the theories of incompressible porous elastic medium and random vibration,on the premises of Kirchhoff assumption and small deformation,according to the mathematical model for the bending of saturated incompressible porous plates,a random vibration equation for the transverse bending of fluid-saturated porous elastic plates was established with a concentrated load under the condition of in plane diffusion of pore fluid.Through the analysis on the displacement response of plate and the solid phase moment response of cross section,the power spectral density function and the variance as well as other digital features of the displacement and moment responses of a simply supported plate were obtained when the concentrated load is a stationary random process.As a numerical example,the saturated porous simply supported plate under the concentrated load with an ideal white noise stationary randomness was considered,the power spectral density functions of the displacement and moment response were analyzed and the damping effect of the fluid-solid coupling term on the plate displacement and bending moment was discussed.The results show that the random vibration of the plate could be controlled by changing the permeability coefficient of the pore fluid.%在不可压多孔弹性介质理论和随机振动理论的基础上,以Kirchhoff假定和小变形为前提,根据饱和不可压多孔板弯曲的数学模型,针对孔隙流体沿面内扩散的情形,建立了含液饱和多孔弹性板在集中荷载作用下横向弯曲的随机振动方程.针对四边简支矩形板,对板内位移响应和截面固相弯矩响应进行了分析,分别得到了输入集中荷载为平稳随机过程时简支板的位移响应和弯矩响应的功率谱密度函数和方差等数字特征.作为数值算例,考虑一理想白噪声平稳随机集中荷载作用下的简支饱和多孔板,对其位移响应和界面固相弯矩的功率谱密度函数进行了分析,并讨论了流-固耦合项对板位移以及弯矩的影响规律.结果表明,通过调整孔隙中流体的渗透系数可以达到控制板随机振动的目的.