Free vibration analysis of corrugated-core sandwich plates using a meshfree Galerkin method based on the first-order shear deformation theory

Abstract

This paper focuses on free vibration analysis of corrugated-core sandwich plates (CSP) via a meshfree Galerkin method based on a first-order shear deformation theory (FSDT). A CSP is considered as a composite structure of three members — two face sheets at the top and the bottom, and one corrugated sheet in the middle of the structure. The face sheets are taken as isotropic plates, and the corrugated sheet is approximated by an orthotropic plate that has different elastic properties along the two perpendicular directions. Dynamic equations of the members are given by the meshfree Galerkin method based on the FSDT. After overcoming the difficulty to implement the displacement compatibility conditions among the members, the governing equation for the entire CSP is obtained by superposing the dynamic equations of the members. The meshfree characteristic of the proposed method guarantee that no meshes are used in deriving the dynamic equations, therefore the proposed method is more flexible in studying problems for which remeshing is inevitable with the finite element methods. The approximation of the corrugated sheet with an orthotropic plate also simplifies the analysis without much loss of precision. A few selected examples are studied to demonstrate the accuracy and convergence of the proposed method. The results obtained for these examples are compared with the ANSYS solutions. Good agreement is evident for all cases.