Finite element analysis of a thin piezoelectric bimorph with a metal shim using solid direct-piezoelectric and shell inverse-piezoelectric coupling with pseudo direct-piezoelectric evaluation

摘要

A thin triple-layer piezoelectric bender, also known as a piezoelectric bimorph with a metal shim, consists of an elastic layer (metal shim) sandwiched between two piezoelectric layers. It is one of the most commonly used piezoelectric composite structures in both sensing and actuation applications. Therefore, this study deals with the coupled piezoelectric-structure interaction analysis of a thin piezoelectric bimorph with a metal shim. In this work, the best features of the solid and shell elements were combined to analyze the piezoelectric and structural fields, respectively, in a thin piezoelectric bimorph with a metal shim. This approach addresses the shortcomings of using a single finite element mesh for both the piezoelectric and structural fields. A transformation method using the block Gauss-Seidel algorithm is employed to exchange the variables between solid direct-piezoelectric and shell inverse-piezoelectric analyses. The metal layer can be analyzed as an elastic body with electrical boundary conditions. A pseudo direct-piezoelectric evaluation method for the metal shim in the piezoelectric analysis is proposed. This method allows us to reuse the existing piezoelectric analysis program, where the metal shim is analyzed as the pseudo direct-piezoelectric material in a single analysis procedure. The homogenization method for the evaluation of bending rigidity and mass is used for modeling the single shell structure in the inverse-piezoelectric analysis of a thin piezoelectric bimorph with a metal layer. Numerical results are given for various electrical configurations of actuators and sensors to validate the present method. Comparison with an exact solution illustrates the accuracy, efficiency, and capability of the developed solid direct and shell inverse-piezoelectric analysis coupled with a pseudo direct-piezoelectric evaluation method to capture the sensor and actuator response of a thin piezoelectric bimorph with a metal shim.