Deterministic and band-limited stochastic energy harvesting from uniaxial excitation of a multilayer piezoelectric stack

Abstract

Deterministic and band-limited stochastic energy harvesting scenarios using a multilayer piezoelectric stack configuration are investigated for uniaxial dynamic pressure loading. The motivation for exploring this off-resonant energy harvesting problem derives from typical civil infrastructure systems subjected to dynamic compressive forces in deterministic or stochastic forms due to vehicular or human loads, among other examples of compressive loading. Modeling of vibrational energy harvesters in the existing literature has been mostly focused on deterministic forms of mechanical vibration as in the typical case of harmonic excitation, while the efforts on stochastic energy harvesting have thus far considered second-order systems such as piezoelectric cantilevers. In this paper, we present electromechanical modeling, analytical and numerical solutions, and experimental validations of piezoelectric energy harvesting from harmonic, periodic, and band-limited stochastic excitation of a multilayer piezoelectric stack under axial compressive loading in the off-resonant low-frequency range. The deterministic problem employs the voltage output-to-pressure input frequency response function of the harvester for a given electrical load, which is also extended to periodic excitation. The analytical stochastic electromechanical solution employs the power spectral density of band-limited stochastic excitation to predict the expected value of the power output. The first one of the two numerical solution methods uses the Fourier series representation of the excitation history to solve the resulting ordinary differential equation, while the second method employs an Euler–Maruyama scheme to directly solve the governing electromechanical stochastic differential equation. The electromechanical models are validated through several experiments for a multilayer PZT-5H stack under harmonic and band-limited stochastic excitations at different pressure levels. The figure of merit is also extracted for this particular energy harvesting problem to choose the optimal material. Soft piezoelectric ceramics (e.g. PZT-5H and PZT-5A) offer larger power output as compared to hard ceramics (e.g. PZT-8), and likewise, soft single crystals (e.g. PMN-PT and PMN-PZT) produce larger power as compared to their hard counterparts (e.g. PMN-PZT-Mn); and furthermore, single crystals (e.g. PMN-PT and PMN-PZT) generate more power than standard ceramics (e.g. PZT-5H and PZT-5A) for low-frequency, off-resonant excitation of piezoelectric stacks.