Modeling and characterization of a piezoelectric energy harvester under combined aerodynamic and base excitations

This paper develops and validates an aero-electromechanical model which captures the nonlinear response behavior of a piezoelectric cantilever-type energy harvester under combined galloping and base excitations. The harvester consists of a thin piezoelectric cantilever beam clamped at one end and rigidly attached to a bluff body at the other end. In addition to the vibratory base excitations, the beam is also subjected to aerodynamic forces resulting from the separation of the incoming airflow on both sides of the bluff body which gives rise to limit-cycle oscillations when the airflow velocity exceeds a critical value. A nonlinear electromechanical distributed-parameter model of the harvester under the combined excitations is derived using the energy approach and by adopting the nonlinear Euler-Bernoulli beam theory, linear constitutive relations for the piezoelectric transduction, and the quasi-steady assumption for the aerodynamic loading. The resulting partial differential equations of motion are discretized and a reduced-order model is obtained. The mathematical model is validated by conducting a series of experiments at different wind speeds and base excitation amplitudes for excitation frequencies around the primary resonance of the harvester. Results from the model and experiment are presented to characterize the response behavior under the combined loading.