Extension of Rayleigh–Ritz method for eigenvalue problems with discontinuous boundary conditions applied to vibration of rectangular plates

Gavalas, George R.; El‐Raheb, Michael

doi:10.1016/j.jsv.2014.03.030

Cited by 2 publications

(1 citation statement)

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“…Bahrami et al [7] have attempted to predict the model properties of free-free FRP plates using the Finite Element Method. Ritz's method is a well-known approximate method used for over a century in classical mechanics and has been successfully implemented in the vibration analysis of beams and plates [8,9]. This method with geometrically admissible functions always gives upper-bound solutions.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Orthotropic Rectangular Plates Using the Ritz Numerical Method

Dileep Kumar

2023

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The main objective of this paper is to contribute to a better understanding of the dynamic response of FRP rectangular plates through modal analysis. The Ritz’s approximation method originated from the principle of minimum potential energy and was chosen to formulate the Eigenvalue problem. The natural frequencies and mode shapes are determined for the first 36 free vibration modes by assuming the double Fourier series functions for the transverse displacement. The most common Beam functions are used as a functional basis. Results are shown for the specific plate problem of Angle ply rectangular plate clamped at one edge, supported at two adjacent edges, and accessible at another edge (CSSF). It is observed that maximum natural frequencies are obtained under the clamped boundary of the plate on all edges of (CCCC) for the rectangular laminates.

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Section: Introductionmentioning

confidence: 99%