Hierarchically decomposed finite element method for a triply coupled piezoelectric, structure, and fluid fields of a thin piezoelectric bimorph in fluid

This paper proposes a numerical method for analyzing a thin piezoelectric bimorph in fluid. A hierarchically decomposed finite element method (FEM) is proposed for modeling the triply coupled piezoelectric-structure–fluid interaction. The electromechanical coupling (piezoelectric-structure interaction) behavior in a thin piezoelectric bimorph is described by the classical constitutive equation, the incompressible fluid flows by the Navier–Stokes equation and the structure by the Cauchy equation of motion. The piezoelectric-structure–fluid interaction system is decomposed into subsystems of fluid–structure interaction (FSI) and piezoelectric field, then the piezoelectric field and the FSI are coupled using the block Gauss–Seidel method, the fluid–structure interaction is split into the fluid–structure velocity field and the pressure field using an algebraic splitting and the fluid–structure velocity field is partitioned into fluid velocity field and structure velocity field. Using the proposed method, the resonance characteristics of a piezoelectric bimorph cantilever made of PVDF and PZT-5H material in fluid are investigated for actuation and sensor configurations.