Strongly coupled partitioned iterative method for the structure–piezoelectric–circuit interaction using hierarchical decomposition

Abstract

The key to the design of advanced micro electro–mechanical devices is an accurate evaluation of the circuit-integrated piezoelectric oscillator that accounts for its complicated configuration. Here, the direct numerical modeling of this oscillator leads to a general formulation as a structure–piezoelectric–circuit interaction. Hence, this study developed a strongly coupled partitioned iterative method for the structure–piezoelectric–circuit interaction. The proposed method was constructed using hierarchical decomposition, the partitioned iterative method for two coupled fields, and loop union. That is, the whole system of the coupled multiphysics is hierarchically decomposed into coupled two-field subsystems, partitioned iterative algorithms for two coupled fields are applied to these subsystems, and the coupling algorithms for these subsystems are reduced to a single coupling algorithm. In the proposed method, three distinct direct piezoelectric, inverse piezoelectric, and circuit solvers are strongly coupled with each other. The inverse piezoelectric solver uses shell finite elements to analyze the response of the thin oscillator efficiently, while the direct piezoelectric solver uses solid finite elements to accurately describe the three-dimensional distribution of the electric potential in the piezoelectric continuum. The proposed method can accurately analyze coupling phenomena in the RC circuit, piezoelectric shunt damping, and piezoelectric energy harvesting.