Flexural vibrations of poroelastic plates

Theodorakopoulos, D.D.; Beskos, D.E.

doi:10.1007/bf01180226

Cited by 76 publications

(43 citation statements)

References 22 publications

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“…Energy dissipation by viscous friction is included through the use of a dynamic #uid density. The calculated de#ection compares very well with the numerical results of reference [6]. The simplicity of the equations obtained gives a better understanding of the physical phenomena involved in the vibration.…”

Section: Introductionmentioning

confidence: 52%

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Transverse Vibrations of a Thin Rectangular Porous Plate Saturated by a Fluid

Leclaire

Horoshenkov

Cummings

2001

Journal of Sound and Vibration

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A simple model of the transverse vibrations of a thin rectangular porous plate saturated by a #uid is proposed. The model is based on the classical theory of homogeneous plates and on Biot's stress}strain relations in an isotropic porous medium with a uniform porosity. Two coupled dynamic equations of equilibrium relating the plate de#ection and the #uid/solid relative displacement are found and their physical interpretation is given. The energy dissipation by viscous friction is included in the model. An approximate calculation of the natural frequencies of vibration is given for rigid plates with various boundary conditions at the edges. The in#uence of porosity, tortuosity and permeability on the resonances is studied and a condition of maximum damping involving these parameters is given.

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Section: Introductionmentioning

confidence: 52%

“…A rigorous and detailed analytical description of this problem including Biot's equations of poroelasticity has been given by Theodorakopoulos and Beskos [6]. In the present article, an additional assumption valid for thin plates is made and an alternative form of the stress}strain relations introduced by Biot [7,8] is used.…”

Section: Introductionmentioning

confidence: 99%

Transverse Vibrations of a Thin Rectangular Porous Plate Saturated by a Fluid

Leclaire

Horoshenkov

Cummings

2001

Journal of Sound and Vibration

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“…Therefore, the deflection w and equivalent moment M p can be solved from (14) and (15). The relative velocitiesw L ( = 1, 2) can be solved from (7b).…”

Section: Fundamental Equations Of Poroelastic Platementioning

confidence: 99%

The fundamental solution of poroelastic plate saturated by fluid and its applications

Wen

Liu

2009

Num Anal Meth Geomechanics

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SUMMARYIn this paper, the numerical model of the transverse vibrations of a thin poroelastic plate saturated by a fluid was proposed. Two coupled dynamic equations of equilibrium related to the plate deflection and the equivalent moment were established for an isotropic porous medium with uniform porosity. The fundamental solutions for a porous plate were derived both in the Laplace transform domain and in the time domain. A meshless method was developed and demonstrated in the Laplace transform domain for solving two coupled dynamic equations. Numerical examples demonstrated the accuracy of the method of the fundamental solutions and comparisons were made with analytical solutions. The proposed meshless method was shown to be simple to implement and gave satisfactory results for a poroelastic plate dynamic analysis.

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“…For a simply supported plate, the integrals take a simple form and a solution similar to Navier's algebraic solution [3] for a porous plate [1] is obtained.…”

Section: Solutionsmentioning

confidence: 99%

“…The vibration of porous beams and plates has been scarcely studied analytically to date. A recent and signi"cant result has been given by Theodorakopoulos and Beskos [1], who have extended the classical theory of thin rectangular plates to porous materials including Biot's stress}strain relations in porous media [2]. They have established two coupled governing equations and have given the solutions for a simply supported plate by extending Navier's algebraic solution [3] to the porous case.…”

Section: Introductionmentioning

confidence: 99%