A unified solution for in-plane vibration analysis of composite laminated sector and annular plate with elastic constraints

Xianlei Guan,Bin Qin,Qingshan Wang,Rui Zhong

doi:10.1177/1461348421994419

Abstract

A semi-analytical method for in-plane vibration analysis of a composite laminated annular and sector plate with elastic constraints is presented. The theoretical model is on the basis of a variational method and a multi-segment technique. Displacement variables are expanded by the Jacobian orthogonal polynomial. Boundary conditions and continuity conditions between segments are characterized by penalty parameters. On this basis, a series of numerical examples are given. The results show that the method has good convergence speed and accuracy. Finally, the parametric study of geometric and material parameters is carried out to provide important support for solving the in-plane characteristics of this kind of composite structure.

Highlights

With the development of science and technology, the preparation technology and equipment of composite materials have made great progress, so the application prospect of composite materials is very promising
For elastic plate and shell structures, their vibration forms can be divided into two types: one is the transverse vibration formed by bending wave, the other is the in-plane vibration caused by the longitudinal wave
The results show that in-plane vibration is very important in some specific high frequency regions.[1]

Summary

Introduction

With the development of science and technology, the preparation technology and equipment of composite materials have made great progress, so the application prospect of composite materials is very promising. Malekzadeh[16] proposed an accurate and efficient solution procedure to study the free vibration of thick laminated annular sector plates on the basis of three-dimensional elasticity theory. In the framework of the firstorder shear deformation plate theory, Belardi et al.[17,18] discussed free vibration characteristics of composite circular plates undergoing transversal loads according to Ritz method As mentioned above, it is the in-plane analysis that is very important in the early design for the composite laminated annular sector plate, circular sector plate, annular plate and circular plate. A variational method and a multi-segment partitioning technique are introduced for the theoretical model of plates based on the first-order shear deformation shell theory, where the latter was originally developed by the author and coworkers for the dynamic analysis of composite laminated doubly-curved shells of revolution.[19,20] The displacement components are expanded by Jacobian orthogonal polynomials. The energy functional of composite laminated annular sector plate and composite laminated annular plate are, respectively, expressed as follows

Nu ðTi

A16 A26 A66

Conclusions