Linear Vibration of Rectangular Plate Resting on Translational And Rotational Supports At All Edges

 International Journal of Engineering Trends and Technology (IJETT) © 2021 by IJETT Journal Volume-69 Issue-2 Year of Publication : 2021 Authors : Ahmed Babahammou, Rhali Benamar DOI :  10.14445/22315381/IJETT-V69I2P201

Citation

MLA Style: Ahmed Babahammou, Rhali Benamar  "Linear Vibration of Rectangular Plate Resting on Translational And Rotational Supports At All Edges" International Journal of Engineering Trends and Technology 69.2(2021):1-11.

APA Style:Ahmed Babahammou, Rhali Benamar. Linear Vibration of Rectangular Plate Resting on Translational And Rotational Supports At All Edges  International Journal of Engineering Trends and Technology, 69(2),1-11.

Abstract
In this paper, the linear free vibrations analysis of rectangular plate resting on translational and rotational supports at all edges is performed by the semi-analytical method. The Rayleigh-Ritz method is used to investigate linear frequencies and associated mode shapes. The trial plate functions are taken as products of beam function with appropriate end conditions in x and y-direction. These beam functions have the form of the solution of the differential equation, which governs their vibrations. A symbolic calculation was used to find the transcendental equation solving the frequency parameters and mode shapes, and the numerical calculation has allowed finding the numerical beam results. The method used in this work does not respect the plate boundary conditions. However, the results of classical boundary conditions, including the guided case, were in good agreement with the bibliography. Moreover, different finite values of the torsional and translation springs stiffness are studied for several values of the aspect ratio. The results found were compared with the available bibliography; both results match with each other very well.

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Keywords
Rectangular plates, Elastically Restraints, Rayleigh-Ritz method, Linear vibration, Frequency parameters.