Performance Evaluation of Numerical Finite Element Coupled Algorithms for Structure–Electric Interaction Analysis of MEMS Piezoelectric Actuator

Abstract

This work presents multiphysics numerical analysis of piezoelectric actuators realized using the finite element method (FEM) and their performances to analyze the structure-electric interaction in three-dimensional (3D) piezoelectric continua. Here, we choose the piezoelectric bimorph actuator without the metal shim and with the metal shim as low-frequency problems and a surface acoustic wave device as a high-frequency problem. More attention is given to low-frequency problems because in our application micro air vehicle’s wings are actuated by piezoelectric bimorph actuators at low frequency. We employed the Newmark’s time integration and the central difference time integration to study the dynamic response of piezoelectric actuators. Monolithic coupling, noniterative partitioned coupling and partitioned iterative coupling schemes are presented. In partitioned iterative coupling schemes, the block Jacobi and the block Gauss–Seidel methods are employed. Resonance characteristics are very important in micro-electro-mechanical system (MEMS) applications. Therefore, using our proposed coupled algorithms, the resonance characteristics of bimorph actuator is analyzed. Comparison of the accuracy and computational efficiency of the proposed numerical finite element coupled algorithms have been carried out for 3D structure–electric interaction problems of a piezoelectric actuator. The numerical results obtained by the proposed algorithms are in good agreement with the theoretical solutions.

Importance of Three-Dimensional Piezoelectric Coupling Modeling in Quantitative Analysis of Piezoelectric Actuators

“…The performance comparison of the several coupling methods including the strong coupling method used here, the monolithic method, and the explicit method was conducted in our previous study for the purpose of illustrating the relative merit and demerit of these methods [21]. Sections 3 and 4 include the basic validation of two coupling method, which was conducted using the theoretical solution.…”

“…Numerical studies often introduce simplified modeling such as order reduction of piezoelectric effects for electric circuit elements [17,18] and weakly coupled DPE and IPE [19,20]. Several algorithms for strongly coupled DPE and IPE have been compared with each other [21]. The partitioned method can be effectively used for a thin piezoelectric bimorph plate analysis [22].…”

One-wing polymer micromachined transmission for insect-inspired flapping wing nano air vehicles

“…The maximum reaction force for u x =0 and the maximum u x when no mechanical load is applied by the piezoelectric bimorph actuator in figure 8 can be obtained theoretically using the following equations [42]: where d 31 =1.98×10 −10 m V −1 is the piezoelectric constant, L=20 mm is the length of the actuator, E p =61 GPa is the Young's modulus of the piezoelectric material, E m =140 GPa is the Young's modulus of the metal shim, t p =0.2 mm is the thickness of the piezoelectric material, t m =0.1 mm is the thickness of the metal shim, w=3 mm is the width of the actuator, and V=200 V is the applied voltage. It should be noted that, to maximize the translational displacement from the biomorph actuator, it should be connected in parallel as shown in figure 8, because this maximizes the biomorph actuator deflection [43]. Figures 9 and 10 show the finite element analysis results.…”

Hierarchical Modeling and Finite Element Analysis of Piezoelectric Energy Harvester From Structure-Piezoelectric-Circuit Interaction

“…This type of framework can be seen repeatedly in coupled multiphysics problems, such as the fluid-structure-electrostatic interaction [5] and the fluid-structure-piezoelectric interaction [6][7][8][9], as well as the structure-piezoelectriccircuit interaction [10]. The inverse piezoelectric solver uses shell finite elements to solve thin FPED, and the direct piezoelectric solver uses solid finite elements to solve an arbitrary three-dimensional distribution of the electrical potential in the piezoelectric continuum accurately [11,12]. The quantities are exchanged between these solvers using block Gauss-Seidel iterative methods (BGS) [13].…”

“…The inverse piezoelectric solver uses shell finite elements to solve thin FPED, and the direct piezoelectric solver uses solid finite elements to solve an arbitrary three-dimensional distribution of the electrical potential in the piezoelectric continuum accurately [11,12]. The quantities are exchanged between these solvers using block Gauss-Seidel iterative methods (BGS) [13]. The electrical potential and charge within the electrode layers are unknown in the cases of an open circuit.…”