Free In-Plane Vibrations of Orthotropic Rectangular Plates by Using an Accurate Solution

Yuan Cao,Qingshan Wang,Dong Shao,Rui Zhong,Dongtao Wu

doi:10.1155/2019/4687082

Abstract

Many numerical methods have been developed for in-plane vibration of orthotropic rectangular plates with various boundary conditions; however, the exact results for such structures with elastic boundary conditions are very scarce. Therefore, the object of this paper is to present an accurate solution for free in-plane vibration of orthotropic rectangular plates with various boundary conditions by the method of reverberation ray matrix (MRRM) and improved golden section search (IGSS) algorithm. The boundary condition studied in this paper is defined as that a set of opposite edges is with one kind of simply supported boundary conditions, while the other set is with any kind of classical and general elastic boundary conditions or their combination. Its accuracy, reliability, and efficiency are verified by some numerical examples where the results are compared with other exact solutions in the published literature and the FEA results based on the ABAQUS software. Finally, some new accurate results for free in-plane vibration of orthotropic rectangular plates with elastic boundary conditions are examined and further can be treated as the reference data for other approximate methods or accurate solutions.

Highlights

Many numerical methods have been developed for in-plane vibration of orthotropic rectangular plates with various boundary conditions; the exact results for such structures with elastic boundary conditions are very scarce. erefore, the object of this paper is to present an accurate solution for free in-plane vibration of orthotropic rectangular plates with various boundary conditions by the method of reverberation ray matrix (MRRM) and improved golden section search (IGSS) algorithm. e boundary condition studied in this paper is defined as that a set of opposite edges is with one kind of supported boundary conditions, while the other set is with any kind of classical and general elastic boundary conditions or their combination
Based on the dynamic stiffness method, Nefovska-Danilovic and Petronijevic [22] carried out the in-plane free vibration and response analysis of isotropic rectangular plates, in which the numerical results were very consistent with finite element method (FEM)
Based on the method of reverberation ray matrix (MRRM) and improved golden section search (IGSS) algorithm, an accurate solution is proposed and free in-plane vibration of orthotropic rectangular plates subjected to various boundary conditions is studied. e boundary condition is defined as that a set of opposite edges are with one kind of supported boundary conditions, where the rest two edges are arbitrary boundary conditions

Summary

Introduction

Many numerical methods have been developed for in-plane vibration of orthotropic rectangular plates with various boundary conditions; the exact results for such structures with elastic boundary conditions are very scarce. erefore, the object of this paper is to present an accurate solution for free in-plane vibration of orthotropic rectangular plates with various boundary conditions by the method of reverberation ray matrix (MRRM) and improved golden section search (IGSS) algorithm. e boundary condition studied in this paper is defined as that a set of opposite edges is with one kind of supported boundary conditions, while the other set is with any kind of classical and general elastic boundary conditions or their combination. Many numerical methods have been developed for in-plane vibration of orthotropic rectangular plates with various boundary conditions; the exact results for such structures with elastic boundary conditions are very scarce. Some new accurate results for free in-plane vibration of orthotropic rectangular plates with elastic boundary conditions are examined and further can be treated as the reference data for other approximate methods or accurate solutions. Du et al [12] studied the in-plane vibration of isotropic rectangular plates with elastically restrained edges by the Rayleigh–Ritz method in conjunction with the Fourier series method. Based on the dynamic stiffness method, Nefovska-Danilovic and Petronijevic [22] carried out the in-plane free vibration and response analysis of isotropic rectangular plates, in which the numerical results were very consistent with FEM. As far as authors know, only “comprehensive exact solutions for free in-plane vibrations of orthotropic rectangular plates” [26]

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Conclusion