Semianalytical piezoelastic solution of orthotropic circular cylindrical panel using SBFEM: Bending and free vibrations

Abstract

A high-performance semi-analytical formulation based on the three-dimensional piezoelectricity theory for bending response and free vibration analysis of circular cylindrical piezoelectric panel subjected to the mechanical and electrical loads is presented. To ensure the accuracy and reliability for the proposed method, a normalized formulation is applied for the constitutive equation of the circular cylindrical piezoelectric panel. By using the scaled boundary finite element method (SBFEM), the normalized dynamic equilibrium equation of cylindrical piezoelectric panel structures in the absence of body force and electric charge is derived into a second-order ordinary differential equation with the analytical form through the weighted residual technique. Under the formulation of the SBFEM, meshes only employed to the boundary of computational domain lead to a reduction of the spatial dimensions by one, so that computation costs can be significantly cut down. After then, the dynamic stiffness equation of whole system is obtained by introducing an intermediate variable. For the static responses, in order to accurately describe the bending behaviors involving the generalized strains and stresses through the thickness, a quadratic function is performed to approximate the generalized displacement vector in the radial direction. For the analysis of free vibrations, the governing equation of motion is rewritten in the expanded form and a condensation of the electric potential degree of freedom is conducted in the system. In this way, the free vibration response of the circular cylindrical piezoelectric panel can be determined by solving the associated eigenvalue problem. Studies of validation and convergence are presented by comparing with those of the published work in which both static and free vibration tests are taken into consideration, and the results show good and convergent performances. Finally, effects of geometric parameters as well as loading conditions on the response characteristics of system are discussed in detail.