A lumped-parameter coupled electro-piezo-aeroelastic model for flapping wings

Abstract

Induced-strain actuated flapping wings and fins, achieved by surface-mounted piezoelectric actuators, do not need conventional motors and mechanisms, potentially reducing system weight, energy consumption, and mechanical complexity compared to conventional systems. A piezocomposite flapping wing or an underwater oscillating fin with induced-strain actuation can interact with the ambient fluid to yield flow vectoring, control, and lift or thrust generation. In this article, an electro-piezo-aeroelastic coupled lumped-parameter model is developed to predict the dynamic behavior of strain actuated flapping wings, and obtain insight into coupling mechanisms such as bend-twist coupling, fluid-structure interaction, and electro-piezo coupling. The piezoelectric wing is modeled as a laminated orthotropic plate. Using the Rayleigh-Ritz method, the distributed wing motion can be represented by lumped wing heave, chordwise curvature, and pitch displacements by assuming prescribed deformation shapes. The assumed shapes are compatible with the fluid effects interpreted as translational and torsional added mass and damping to the structure. The aeroelastic model is then coupled to the circuit model via electro-piezo coupling. The mechanical model is validated using the finite element method. It is found that four wing tip parameters, including first and second order heave motion, pitch, and chordwise curvature are sufficient to represent the wing motion. The lumped parameter wing model is then used to investigate the system optimal parameters for maximizing desired aero- and/or hydro-dynamic responses. System properties such as structural parameters, excitation frequency ratio, etc., are under investigation. The lumped parameter model is computationally efficient, and suitable for trade studies and multi-disciplinary design optimization. Also, the lumped parameter model serves as a foundation for flapping flight analysis, e.g., analyzing lift force, leading-edge vortex stabilization, and tip vortex shedding.