Modeling and Analysis of Piezoelectric Energy Harvesting Beams Using the Dynamic Stiffness and Analytical Modal Analysis Methods

Abstract

The modeling and analysis of base-excited piezoelectric energy harvesting beams have attracted many researchers with the aim of predicting the electrical output for a given base motion input. Despite this, it is only recently that an accurate model based on the analytical modal analysis method (AMAM) has been developed. Moreover, single-degree-of-freedom models are still being used despite the proven potential for significant error. One major disadvantage of the AMAM is that it is restricted to simple cantilevered uniform-section beams. This paper presents two alternative modeling techniques for energy harvesting beams and uses these techniques in a theoretical study of a bimorph. One of the methods is a novel application of the dynamic stiffness method (DSM) to the modeling of energy harvesting beams. This method is based on the exact solution of the wave equation and so obviates the need for modal transformation. The dynamic stiffness matrix of a uniform-section beam could be used in the modeling of beams with arbitrary boundary conditions or assemblies of beams of different cross sections. The other method is a much-needed reformulation of the AMAM that condenses the analysis to encompass all previously analyzed systems. The Euler–Bernoulli model with piezoelectric coupling is used and the external electrical load is represented by generic linear impedance. Simulations verify that, with a sufficient number of modes included, the AMAM result converges to the DSM result. A theoretical study of a bimorph investigates the effect of the impedance and quantifies the tuning range of the resonance frequencies under variable impedance. The neutralizing effect of a tuned harvester on the vibration at its base is investigated using the DSM. The findings suggest the potential of the novel concept of a variable capacitance adaptive vibration neutralizer that doubles as an adaptive energy harvester. The application of the DSM to more complex systems is illustrated. For the case studied, a significant increase in the power generated was achieved for a given working frequency through the application of a tip rotational restraint, the use of segmented electrodes, and a resized tip mass.