含液饱和不可压多孔弹性板的随机振动

周凤玺1,2?,李丹1,曹小林1

振动与冲击 ›› 2017, Vol. 36 ›› Issue (10) : 168-174.

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振动与冲击 ›› 2017, Vol. 36 ›› Issue (10) : 168-174.
论文

含液饱和不可压多孔弹性板的随机振动

  • 周凤玺1,2?,李丹1,曹小林1
作者信息 +

Random vibration of fluid-saturated porous elastic plate

  • ZHOU Feng-xi1,2, LI Dan1, CAO Xiao-lin1
Author information +
文章历史 +

摘要

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。

Abstract

On the basis of the theory of incompressible porous elastic medium and random vibration, on the premise of kirchhoff assumption and small deformation, according to the mathematical model of Saturated incompressible porous plate bending, the random vibration equation of transverse bending on fluid-saturated porous elastic plate were established with the concentrated load under the condition of diffusion of pore fluids along the plane direction. Through the analysis on the response of both the displacement of plate and the solid moment of cross section, the power spectral density function and variance and other digital features of the displacement and the moment response on the simply supported plate could be obtained when the input of concentrated load is stationary random process. As a numerical example, considering saturated porous simply supported plate under the concentrated load in an ideal white noise stationary random, the power spectral density function of the displacement response and the interface solid moment were analyzed and the damping effect of the flow-solid coupling term on the board displacement and bending moment were also discussed. The results showed that random vibration in the plate could be controlled by changing the coefficient of permeability in the pore fluid.

关键词

多孔介质理论 / 随机振动 / 功率谱密度函数 / 四边简支板

Key words

porous media theory / random vibration / power spectral density function / simply supported plate

引用本文

导出引用
周凤玺1,2?,李丹1,曹小林1. 含液饱和不可压多孔弹性板的随机振动[J]. 振动与冲击, 2017, 36(10): 168-174
ZHOU Feng-xi1,2, LI Dan1, CAO Xiao-lin1. Random vibration of fluid-saturated porous elastic plate[J]. Journal of Vibration and Shock, 2017, 36(10): 168-174

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