Electroelastic Modeling and Experimental Validation of Piezoelectric Energy Harvesting From Broadband Random Vibrations

Energy harvesting from ambient environment has received increasing attention over the last decade due to the need for minimizing the dependence on conventional batteries in wireless applications. Among the methods of vibration-to-electricity conversion, piezoelectric transduction has been investigated by numerous research groups due to the ease of application and high power density offered by piezoelectric materials. Electromechanical modeling efforts of piezoelectric energy harvesters have been mostly focused on deterministic forms of excitation input, as in the typical case of harmonic excitation. In most practical applications, however, ambient vibrational energy is often stochastic with broad frequency content. This paper presents analytical and numerical modeling, simulations, and experimental validations of piezoelectric energy harvesting from broadband random vibrations. The models employed herein are based on distributed-parameter electroelastic solution to ensure that the effects of higher vibration modes are included. The goal is to predict the expected value of the power output in terms of the given power spectral density (PSD) or time history of the random vibration input. The analytical estimations are based on the PSD of broadband random base excitation and distributed-parameter frequency response functions (FRFs) of the coupled voltage and vibration response. The numerical simulations use the Fourier series representation of base acceleration history in an ordinary differential equation solver that employs first-order electroelastic equations. The simulations are compared against the experiments for a brass-reinforced PZT-5H bimorph under different random excitation levels. The analytical and numerical simulations exhibit very good agreement with the experimental measurements. Soft and hard ceramic and single crystal bimorphs (made of PZT-5H, PZT-8, PMN-PZT, and PMN-PZT-Mn) are compared for broadband random excitation through a theoretical case study.