A reduced-order multi-body model with electromechanical-aeroelastic coupling for mechanism-free ornithopters

Piezoelectric material-actuated so-called solid-state (i.e., mechanism-free) ornithopters do not need conventional motors and mechanisms, potentially saving weight and energy consumption, reducing mechanical complexity, and improving wing flexibility. In solid-state ornithopters, wing flapping can be achieved by surface-mounted piezoelectric actuators. The design of a solid-state ornithopter is a complex multi-disciplinary task, and optimization of wing topology, actuator placement, and excitation parameters requires a computationally efficient model to predict its dynamic response and performance metrics. In this paper, effectively, a novel flight simulation model is presented based on a reduced-order lumped parameter multi-body model coupled with a vortex lattice program. The proposed lumped parameter model can be represented by an equivalent multi-body mechanical model or a circuit model. The coupling considered in the lumped parameter model includes: (1) the body-wing momentum interaction, (2) bend–twist​ coupling of the piezocomposite wings, (3) fluid–structure interactions between the flapping wings, oscillating body, and the ambient fluid, and (4) electromechanical coupling between a resistive–inductive–capacitive driving circuit and the piezocomposite wings. The wing motion is described using the Rayleigh–Ritz method, in which the representative wing modes are identified as spanwise plunge, chordwise curvature, and twist. The body-wing interaction is modeled using Hamilton’s principle. The fluid-induced effects on the wings have three contributions: added mass and damping, quasi-steady aerodynamic forces obtained using the vortex lattice program, and unsteady aerodynamic forces calculated using the Theodorsen formulation, which is integrated into the wing heave and pitch degrees of freedom in the lumped parameter model. The proposed reduced-order model proposed is computationally efficient, suitable for trade studies and multi-disciplinary design optimization, and can be easily converted to state representation for controller development purposes. The capabilities of this model are demonstrated through tethered and gliding flight simulations. System properties such as circuit parameters, structural parameters, excitation frequency ratio, etc., are investigated. Phugoid and short period modes are observed in gliding flight simulations. The contribution of active flapping is found by the comparison of flight simulations with and without active flapping. A net thrust contributed by unsteady lift is demonstrated even though the thrust-lift ratio is low. The proposed model serves as an extensible framework for modeling and design optimization of ornithopters.