Random vibration of fluid-saturated porous elastic plate

PDF(1239 KB)

Journal of Vibration and Shock ›› 2017, Vol. 36 ›› Issue (10) : 168-174.

ZHOU Feng-xi1,2, LI Dan1, CAO Xiao-lin1

Author information +

History +

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.

Key words

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

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

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

References

[1]　de Boer R. Reflections on the development of the theory of porous media[J]. Applied Mechanics Review, 2003, 5 6(6): 27-42.
[2]　Bowen R M. Incompressible porous media models by use of the theory of mixtures[J]. International Journal of Engineering Science，1980, 18: 1129-1148.
[3]　Bowen R M. Compressible porous media models by use of the theory of mixtures[J]. International Journal of Engineering Science, 1982, 20: 697-735.
[4]　Taber L A. A theory for transverse deflection of poroelastic plates[J]. ASME Journal of Applied Mechanics, 1992, 59: 628-634.
[5]　Li L P, Cederbaum G, Schulgasser K. Theory of poroelastic plates with in-plane diffusion[J]. International Journal of Solids and Structures, 1997, 34(35-36): 4515-4530.
[6] Leclaire P, Horoshenkov K V, Cummings A. Transverse vibration of a thin rectangular porous plate saturated by a fluid[J]. Journal of Sound and Vibration, 2001, 247(1): 1-18.
[7]　Leclaire P, Horoshenkov K V, Cummings A. The vibrational response of a clamped rectangular porous plate[J]. Journal of Sound and Vibration, 2001, 247(1): 19-31.
[8] 杨骁,李丽.不可压饱和多孔弹性梁、杆动力响应的数学模型[J]. 固体力学学报,2006, 27(2): 159-166.
YANG Xiao, Li Li. Large deflection analysis of simply supported saturated poroelastic beam[J]. Chinese Journal of Solid Mechanics, 2007, 28(3): 313-3l7
[9] 周凤玺,马强,宋瑞霞. 含液饱和多孔二维梁的动力特性分析[J].工程力学, 2015, 32(5): 198-207.
ZHOU Feng-xi, MA Qiang, SONG Rui-xia. Dynamic response analysis of a two dimensional fluid-saturated porous beam[J]. ENGINEERING MECHANICS, 2015, 32(5):198-207.
[10] 周凤玺,米海珍.弹性地基上不可压含液饱和多孔弹性梁的自由振动[J].兰州理工大学学报，2014, 40(2): 118-122.
ZHOU Feng-xi, MI Hai-zhen. Free vibration of poroelastic beam with incompressible saturated liquidmon elastic foundation[J]. Journal of Lanzhou University of Technology, 2014, 40(2): 118-122.
[11] 周凤玺，马强，米海珍.含液饱和多孔弹性梁的随机振动[J].振动与冲击, 2015, 34(22): 206-209.
ZHOU Feng-xi, MA Qiang, MI Hai-zhen. Random vibratio of fluid-saturated porous elastic beam[J]. Journal of Vibration and Shock , 2015, 34(22): 206-209.
[12] 裴然,杜敬涛,朱明刚,杨铁军.弹性板结构面内振动特性分析与实验研究[J].哈尔滨工程大学学报，2015, 36(4): 1-5.
PEI Ran, DU Jingtao, ZHU Minggang, YANG Tie jun. In -plane modal characteristics of flexible plate structure and its experimental study[J]. Journal of Harbin Engineering University, 2015, 36(4): 1-5.
[13] 薛开,王久法,王威远,李秋红,王平.变厚度薄板在任意弹性边界条件下的自由振动分析[J].振动与冲击，2013, 32(21): 132-137.
XUE Kai, WANG Wei-yuan, LI Qiu-hong, WANG Ping.Free vibration analysis of tapered plates with arbitrary elastic boundary condition[J]. Journal of Vibration and Shock, 2013, 32(21): 132-137.
[14] 李丽，杨骁.简支饱和多孔弹性梁的非线性弯曲[J].力学季刊，2007, 28(1): 86-91.
Li Li, Yang Xiao. Nonlinear bending of simply supported saturated poroelastic beam[J]. Chinese Quarterly of Mechanics, 2007, 28(1): 86-91.
[15] 杨骁，程昌钧.流体饱和多孔介质的动力学Gurtin型变分原理和有限元模拟[J].固体力学报，2003, 24(3): 267-276.
Yang Xiao, Cheng Changjun. Gurtin variational principle and finite element simulation for dynamical problems of fluid-saturated porous media[J]. Acta Mechanica Solida Sinica, 2003, 24: 267-276.
[16] 何录武,杨骁. 饱和不可压多孔弹性板在面内扩散下的动力弯曲理论[J].固体力学学报，2008, 29(2): 121-128.
HE Lu-wu, Yang Xiao. A dynamic bending model of incompressible saturated proelastic plates with in-plane diffusion[J]. Chinese Journal of Solid Mechanics, 2008, 29(2): 121-128.
[17] 欧进萍,王光远.结构随机振动[M]．北京,高等教育出版社，1998.
OU Jin-ping, Wang Guang-yuan. Random vibration of structure[M]．Beijing: Higher Education Press, 1998.
[18] Liu D, Xu W, Xu Y. Stochastic response of an axiall moving viscoelastic beam with fractional order constitutive relationand random excitations[J]. Acta Mechanica Sinica, 2013, 29(3): 443-451.
[19] 刘又文.应用固体力学[M].北京:中国科学文化出版社, 2003.