Free Vibration of Rectangular Plates with Porosity Distributions under Complex Boundary Constraints

Free vibration of rectangular plates with three kinds of porosity distributions and different boundary constraints has been performed by means of a semianalytical method. The distribution of porous varies along the thickness of the plate, in which the mechanical properties are defined by open-cell m...

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Bibliographic Details
Published inShock and vibration Vol. 2019; no. 2019; pp. 1 - 16
Main Authors Shan, Yanhe, Sun, Liping, Wang, Siyu, Du, Yuan
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 2019
Hindawi
John Wiley & Sons, Inc
Hindawi Limited
Wiley
Subjects
Boundary conditions
Force and energy
Fourier series
Free vibration
Kinetic energy
Mechanical properties
Metal foams
Parameters
Porosity
Potential energy
Rectangular plates
Resonant frequencies
Ritz method
Shear deformation
Sine series
Trigonometric functions
Vibration
Iran
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Summary:Free vibration of rectangular plates with three kinds of porosity distributions and different boundary constraints has been performed by means of a semianalytical method. The distribution of porous varies along the thickness of the plate, in which the mechanical properties are defined by open-cell metal foam. Regardless of boundary conditions, displacement admissible functions are represented by combination of standard cosine Fourier series and auxiliary sine series. The kinetic energy and potential energy of plates are also expressed on the basis of first-order shear deformation theory (FSDT) and displacement admissible functions. Finally, the coefficients in the Fourier series which determine natural frequencies and modal shape are derived by means of the Rayleigh–Ritz method. Convergence and dependability of the current method are verified by comparing with the results of FEM and related literatures. In addition, some new results considering geometry parameters under classical and elastic boundary constraints are listed. The effects of geometry parameters, material parameters, and boundary constraints have been discussed in detail.
ISSN:1070-9622
1875-9203
DOI:10.1155/2019/6407174