Electrohydroelastic Euler-Bernoulli-Morison model for underwater resonant actuation of macro-fiber composite piezoelectric cantilevers

Bio-inspired hydrodynamic thrust generation using smart materials has received growing attention over the past few years to enable improved maneuverability and agility, small form factor, reduced power consumption, and ease of fabrication in next-generation aquatic swimmers. In order to develop a high-fidelity model to predict the electrohydroelastic dynamics of macro-fiber composite (MFC) piezoelectric structures, in this work, mixing rules-based (i.e. rule of mixtures) electroelastic mechanics formulation is coupled with the global electroelastic dynamics based on the Euler-Bernoulli kinematics and nonlinear fluid loading based on Morison's semi-empirical model. The focus is placed on the dynamic actuation problem for the first two bending vibration modes under geometrically and materially linear, hydrodynamically nonlinear behavior. The electroelastic and dielectric properties of a representative volume element (piezoelectric fiber and epoxy matrix) between two subsequent interdigitated electrodes are correlated to homogenized parameters of MFC bimorphs and validated for a set of MFCs that have the same overhang length but different widths. Following this process of electroelastic model development and validation, underwater actuation experiments are conducted for different length-to-width aspect ratios (L/b) in quiescent water, and the empirical drag and inertia coefficients are extracted from Morison's equation to establish the electrohydroelastic model. The repeatability of these empirical coefficients is demonstrated for experiments conducted using aluminum cantilevers of different aspect ratios with a focus on the first two bending modes. The convergence of the nonlinear electrohydroelastic Euler-Bernoulli-Morison model to its hydrodynamically linear counterpart for increased L/b values is also reported. The proposed model, its harmonic balance analysis, and experimental results can be used not only for underwater piezoelectric actuation, but also for sensing and energy harvesting problems.