含液饱和多孔弹性梁随机振动

周凤玺1,2，马强1，米海珍1

(1.兰州理工大学土木工程学院，兰州730050； 2. 兰州理工大学西部土木工程防灾减灾教育部工程研究中心，兰州730050)

摘要：据不可压多孔弹性介质理论及随机振动理论，建立孔隙流体沿轴向扩散情形下含液饱和多孔弹性梁在集中荷载作用下横向弯曲随机振动方程。分析梁位移响应及截面固相弯矩响应，获得输入集中荷载为平稳随机过程时简支梁位移、弯矩响应的功率谱密度函数及方差等数字特征。作为数值算例，考虑理想白噪声平稳随机集中荷载作用下的简支饱和多孔梁，分析其位移响应及界面固相弯矩功率谱密度函数，讨论流-固耦合项对梁位移及弯矩的减振效果。结果表明，通过控制孔隙中流体的渗透系数可达到控制梁的随机振动目的。

关键词：多孔介质理论；随机振动；功率谱密度函数；简支梁

中图分类号:O324文献标志码：A

基金项目：国家自然科学基金(51174013)

收稿日期：2015-03-21修改稿收到日期：2015-05-24

Random vibration of fluid-saturated porous elastic beam

ZHOUFeng-xi1,2,MAQiang1,MIHai-zhen1(1. School of Civil Engineering, Lanzhou University of Technology, Lanzhou 730050, China；2. Western Engineering Research Center of Disaster Mitigation in Civil Engineering of Ministry of Education, Lanzhou University of Technology, Lanzhou 730050, China)

Abstract:According to the theory of incompressible porous elastic medium and the random vibration, theory of continum, a random equation for the transverse bending vibration of fluid-saturated porous elastic beam was established with a concentrated load under the condition of diffusion of pore fluid along the axial direction. Through the analysis on the responses of the displacement of beam as well as the solid phase bending moment at cross section of beam, the power spectral density function and its variance and other digital features of the displacement and bending moment responses of a simply supported beam were obtained when the concentrated load is a stationary random process. As a numerical example, considering the saturated porous simply supported beam under the concentrated load of an ideal white noise stationary random process, the power spectral density functions of the displacement response and the interface solid phase bending moment response were analyzed and the damping effects of the flow-solid coupling term on the beam displacement and bending moment were also discussed. The results show that random vibration of the beam could be controlled by changing the coefficient of permeability of the pore fluid.

Key words:porous media theory; random vibration; power spectral density function; simply supported beam

含液饱和多孔介质在岩土、生物及传热传质等众多工程领域中均有重要用途。由于骨架与液体相互作用及两者不同运动特性，含液饱和介质的力学行为与单相介质截然不同，特性独特。自Biot[1-2]提出描述饱和多孔介质动力特性的基本方程以来，均从不同角度对该问题进行研究，但因该理论基础缺乏充分的热力学依据，而使基于连续介质混合物公理及体积分数概念的多孔介质理论与数值方法研究取得长足进展，并广泛用于不同工程领域[3]。……