Abstract
In this paper, free vibration characteristics of laminated composite plates are investigated. A model is developed for a composite layer based on the consideration of non-linear terms in von-Karman’s non-linear deformation theory. The governing partial equation of motion is reduced to an ordinary non-linear equation and then solved using LIM method. The variation of frequency ratio of the Isotropic and composite plates is brought out considering parameters such as aspect ratio, fiber arrangements (orientation), number of layers, and modal ratios.
Highlights
Laminated composite plates, due to their high specific strength and stiffness have been increasingly used in a wide range of aerospace, mechanical, and civil applications
In many working conditions, plates are subjected to large amplitudes, so a nonlinear frequency analysis is required as a result
The first approximate solution developed by Chu and Herman[1] in 1956, was the start point for so many other numerical methods introduced in the following years such as the finite element method (FEM)[2], the discrete singular convolution method (DSC), the strip element method, and the Ritz methods[3]
Summary
Due to their high specific strength and stiffness have been increasingly used in a wide range of aerospace, mechanical, and civil applications. One of the main approximate analytical approaches on nonlinear vibration analysis is Perturbation Method This method is effective just in solving weakly nonlinear differential equations. Pirbodaghi et al.[7] used the homotopy analysis method (HAM) to obtain an approximate analytical solution for nonlinear vibrations of thin laminated composite plates and showed effectiveness of this method to obtain an accurate solution with relatively less computational effort. The energy balance method (EBM) [8], the max-min approach (MMA) [9], the homotopy perturbation method (HPM) [10] and so many others have been proved to be strong approximate analytical approaches, obtaining accurate results for nonlinear differential equations [11]. LIM method is used to obtain approximate analytical solutions for nonlinear vibrations of a thin laminated composite plate. The impact of layer arrangements and aspect ratio effects on the free vibration are investigated in detail
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