Analytical solution for vibration and buckling of annular sectorial porous plates under in-plane uniform compressive loading

Analytical solution for vibration and buckling of annular sectorial porous plates under in-plane... In this article, an analytical solution for free vibration of moderately thick annular sectorial porous plates in the presence of in-plane loading is presented. Because of the in-plane loading, before the vibrational analysis, a buckling analysis is performed. To this end, equations of motion together with the stability equations are derived using Hamilton principle. Both the governing equations of motion and stability are highly coupled differential equations, which are difficult to solve analytically. So, they are decoupled through performing some mathematical operations. The decoupled equations are then solved analytically for annular plates with simply supported boundary conditions on the radial edges and different boundary conditions on the circumferential edges. Natural frequencies and also critical buckling load are obtained and the effects of thickness ratio, radii ratio, porosity, and boundary conditions are studied in detail. Finally, the effect of in-plane loading on the natural frequency of the plate is studied comprehensively. Numerical results show that the natural frequency decreases as the load ratio approaches one and vanishes as it reaches one. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science SAGE

Analytical solution for vibration and buckling of annular sectorial porous plates under in-plane uniform compressive loading

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Publisher
SAGE Publications
Copyright
© IMechE 2017
ISSN
0954-4062
eISSN
2041-2983
D.O.I.
10.1177/0954406217716197
Publisher site
See Article on Publisher Site

Abstract

In this article, an analytical solution for free vibration of moderately thick annular sectorial porous plates in the presence of in-plane loading is presented. Because of the in-plane loading, before the vibrational analysis, a buckling analysis is performed. To this end, equations of motion together with the stability equations are derived using Hamilton principle. Both the governing equations of motion and stability are highly coupled differential equations, which are difficult to solve analytically. So, they are decoupled through performing some mathematical operations. The decoupled equations are then solved analytically for annular plates with simply supported boundary conditions on the radial edges and different boundary conditions on the circumferential edges. Natural frequencies and also critical buckling load are obtained and the effects of thickness ratio, radii ratio, porosity, and boundary conditions are studied in detail. Finally, the effect of in-plane loading on the natural frequency of the plate is studied comprehensively. Numerical results show that the natural frequency decreases as the load ratio approaches one and vanishes as it reaches one.

Journal

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering ScienceSAGE

Published: Jun 1, 2018

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