We present electroelastic modeling, analytical and numerical solutions, and experimental validations of piezoelectric energy harvesting from broadband random vibrations. The modeling approach employed herein is based on a distributed-parameter electroelastic formulation to ensure that the effects of higher vibration modes are included, since broadband random vibrations, such as Gaussian white noise, might excite higher vibration modes. The goal is to predict the expected value of the power output and the mean-square shunted vibration response in terms of the given power spectral density (PSD) or time history of the random vibrational input. The analytical method is based on the PSD of random base excitation and distributed-parameter frequency response functions of the coupled voltage output and shunted vibration response. The first of the two numerical solution methods employs the Fourier series representation of the base acceleration history in an ordinary differential equation solver while the second method uses an Euler-Maruyama scheme to directly solve the resulting electroelastic stochastic differential equations. The analytical and numerical simulations are compared with several experiments for a brass-reinforced PZT-5H bimorph under different random excitation levels. The simulations exhibit very good agreement with the experimental measurements for a range of resistive electrical boundary conditions and input PSD levels. It is also shown that lightly damped higher vibration modes can alter the expected power curve under broadband random excitation. Therefore, the distributed-parameter modeling and solutions presented herein can be used as a more accurate alternative to the existing single-degree-of-freedom solutions for broadband random vibration energy harvesting.

Numerical and experimental investigations of broadband random vibrational energy harvesting using monostable and bistable piezoelectric cantilevers are presented along with relative performance comparisons. Simulations and experiments reveal that a linear-monostable energy harvester can outperform its bistable counterpart for very low and relatively high random excitation levels. The bistable configuration generates more power for a limited excitation intensity range slightly above the threshold of interwell oscillations. Under broadband stochastic excitation, a bistable energy harvester can potentially be preferred only if it is designed to operate at a known excitation intensity, otherwise using a monostable harvester can be more robust and practical.

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Vibration‐based energy harvesting for enabling next‐generation self‐powered devices is a rapidly growing research area. In real‐world applications, the ambient vibrational energy is often available in non‐deterministic forms rather than the extensively studied deterministic scenarios, such as simple harmonic excitation. It is of interest to choose the best piezoelectric material for a given random excitation. Here, performance comparisons of various soft and hard piezoelectric ceramics and single crystals are presented for electrical power generation under band‐limited off‐resonance and wideband random vibration energy‐harvesting scenarios. For low‐frequency off‐resonance excitation, it is found that soft piezoelectric ceramics based upon lead zirconate titanate (e.g., PZT‐5H and PZT‐5A) outperform their hard counterparts (e.g., PZT‐4 and PZT‐8), and likewise soft single crystals based upon lead magnesium niobate and lead titanate as well as PZT (e.g., PMN‐PT and PMN‐PZT) outperform the relatively hard ones (e.g., manganese‐doped PMN‐PZT‐Mn). Overall, for such off‐resonance random vibrations, PMN‐PT is the most suitable choice among the materials studied. For wideband random excitation with a bandwidth covering the fundamental resonance of the harvester, hard piezoelectric ceramics offer larger power output compared to soft ceramics, and likewise hard single crystals produce larger power compared to their soft counterparts. Remarkably, a hard piezoelectric ceramic (e.g., PZT‐8) can outperform a soft single crystal (e.g., PMN‐PT) for wideband random vibration energy harvesting.