A Multi-Mode Approach to Geometrically Nonlinear Free and Forced Vibrations of Rectangular Plate Resting on Two Line Supports
A Multi-Mode Approach to Geometrically Nonlinear Free and Forced Vibrations of Rectangular Plate Resting on Two Line Supports |
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| © 2023 by IJETT Journal | ||
| Volume-71 Issue-4 |
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| Year of Publication : 2023 | ||
| Author : Ahmed Babahammou, Rhali Benamar |
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| DOI : 10.14445/22315381/IJETT-V71I4P236 | ||
How to Cite?
Ahmed Babahammou, Rhali Benamar, "A Multi-Mode Approach to Geometrically Nonlinear Free and Forced Vibrations of Rectangular Plate Resting on Two Line Supports, " International Journal of Engineering Trends and Technology, vol. 71, no. 4, pp. 416-435, 2023. Crossref, https://doi.org/10.14445/22315381/IJETT-V71I4P236
Abstract
Linear and geometrically nonlinear free and forced vibrations analysis by the multi-mode approach of continuous rectangular plates is performed by a semi-analytical method. The Rayleigh-Ritz method is used to calculate the linear frequency parameters and associated mode shapes. The line supports are modeled by distributions of translational springs contributing to the plate strain energy with a stiffness tending to infinity. The choice of the trial functions set presents the novelty of this work. Indeed, this set does not respect the intermediate lines but must only verify the plat boundary conditions. The linear results found are compared to those of previous work to verify the accuracy and reliability of the present formulation. On the other hand, Benamar's method is used to investigate the nonlinear vibrations of the studied plate. A code is performed for this work to use the lsqnonlin routine from Matlab software. This code solves the nonlinear algebraic system using the least squares method. The plotted backbone curves show that the hardening type of the studied plate admits a minimum function of the aspect ratio. The amplitude-dependent nonlinear mode shapes are plotted and discussed. The forced regime was investigated by concentrated and distributed harmonic excitation forces with several levels.
Keywords
Rectangular plates, Intermediate lines, Nonlinear vibrations, Free and forced regime, Bending stress.
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