Transverse Vibration Analysis of Composite Plates with Multiple Distributed Composite Patches

Yan Guo,Bin Huang,Ji Wang,Yanan Jiang,Giosuè Boscato

doi:10.1155/2020/6618983

Abstract

Transverse vibration of rectangular composite plates with multiple distributed composite patches is analyzed in this paper. Because of the geometric discrepancy between the plate and patch, analytical solutions are usually hard to achieve. The present model is formulated by using the Rayleigh–Ritz method and adopting various types of modal shape functions of uniform beam as admissible functions for different boundary conditions. The total system energies are calculated by adding the energies of the substrate plate and the energies of the patches. By imposing the displacement-matching condition at the patch domains, the coordinate systems of the substrate plate and patches are coupled. By means of the present method, it is very convenient and efficient to build the system governing equations and solve the eigenvalue problem. For the composite patches, they are also assumed to be symmetrically layered and have the same layer stacking sequence with the substrate laminate. The effects of layer stacking sequence, modulus ratio, aspect ratio, and boundary conditions on the natural frequencies are investigated and discussed. The results are also compared with the existed benchmark solutions and FEM solutions for validation. The numerical results demonstrate that the proposed approach is computationally very efficient and accurate and can be used as a tool to solve transverse vibration problems of composite plate with multiple composite patches.

Highlights

Composite patch structures have been widely used in the repair of aircraft, marine ships, and so on, and they are usually used to reinforce structures or repair damaged parts [1, 2]
We solve the transverse vibration problem with multiple patches on the substrate laminate. e cross-ply and angle-ply laminates with clamped and supported boundary conditions are chosen for numerical analysis. e effects of parameters, such as patch number and patch size, aspect ratio, and modulus ratio, on the natural frequencies are investigated. e present results are compared with those well-known published results and FEM results. e proposed method is very efficient in predicting the transverse vibration of composite laminates with multiple composite patches and can be used as a design tool for modeling of patched composite structures
E accuracy of the present approach for transverse vibration analysis of composite substrate with distributed multiple composite patches is validated by the finite element method and other existed benchmark solutions

Summary

Introduction

Composite patch structures have been widely used in the repair of aircraft, marine ships, and so on, and they are usually used to reinforce structures or repair damaged parts [1, 2]. Vaziri and Nayeb-Hashemi [26] studied the dynamic response of a repaired composite with bonded patch under a harmonic peeling load and found the elastic modulus of the adhesive layer dominates the mechanism of deformation of the repaired beam and its vibration characteristics. In a word, it can be clearly found there is not many works focusing on the modeling of multiple composite laminated patches on composite substrates considering the effects of both mass and stiffness. We solve the transverse vibration problem with multiple patches on the substrate laminate. e cross-ply and angle-ply laminates with clamped and supported boundary conditions are chosen for numerical analysis. e effects of parameters, such as patch number and patch size, aspect ratio, and modulus ratio, on the natural frequencies are investigated. e present results are compared with those well-known published results and FEM results. e proposed method is very efficient in predicting the transverse vibration of composite laminates with multiple composite patches and can be used as a design tool for modeling of patched composite structures

Mathematical Modeling

Numerical Results

Conclusions