Magneto-electro-elastic semi-analytical models for free vibration and transient dynamic responses of composite cylindrical shell structures

Abstract

Application of the scaled boundary finite element method (SBFEM) in free vibration and transient dynamic problems of the composite magneto-electro-elastic (MEE) cylindrical shell is considered in this paper for the first time. The mathematic model of the composite MEE cylindrical shell is governed by the three-dimensional (3D) theory of magneto-electro-elasticity in the cylindrical coordinate system, and the dynamic equilibrium equations are then derived into a second-order ordinary differential equation by using the SBFEM. In this method, discretizations are confined only to the surfaces or boundaries of the computational domain but no fundamental solutions and singular integrals are required, which reduces the spatial dimension of problem by one and making mesh generation much easier. At the same time, the transverse shear locking can be successfully avoided due to the analyticity of the SBFEM governing equation in the radial direction of the scaled boundary coordinate system. Based on the state space approach, the basic equations of the composite MEE cylindrical shell in the scaled boundary coordinate system are reduced to a system of first-order ordinary differential equation in terms of the independent variable involving the generalized displacement and internal nodal force fields, and then the free vibration and transient dynamic responses of the system are solved by using the generalized eigenvalue technique and Newmark's integration scheme, respectively. Numerical results illustrate that the convergence of the proposed formulations is satisfactory, and excellent agreement can be achieved for limiting cases with the solutions available in published work or that obtained using the commercial software ANSYS. In addition, the influences of the structural parameters (including thickness ratio, aspect ratio and stacking configuration), material properties and boundary conditions on the vibration and dynamic behaviors of the composite MEE cylindrical shells are discussed.