A square cylinder with a V-shaped groove on the windward side in the piezoelectric cantilever flow-induced vibration energy harvester (FIVEH) is presented to improve the output power of the energy harvester and reduce the critical velocity of the system, aiming at the self-powered supply of low energy consumption devices in the natural environment with low wind speed. Seven groups of galloping piezoelectric energy harvesters (GPEHs) were designed and tested in a wind tunnel by gradually changing the angle of two symmetrical sharp angles of the V-groove. The GPEH with a sharp angle of 45° was selected as the optimal energy harvester. Its output power was 61% more than the GPEH without the V-shaped groove. The more accurate mathematical model was made by using the sparse identification method to calculate the empirical parameters of fluid based on the experimental data and the theoretical model. The critical velocity of the galloping system was calculated by analyzing the local Hopf bifurcation of the model. The minimum critical velocity was 2.53 m/s smaller than the maximum critical velocity at 4.69 m/s. These results make the GPEH with a V-shaped groove (GPEH-V) more suitable to harvest wind energy efficiently in a low wind speed environment.

In this work, we propose a wideband quintuple-well potential piezoelectric-based vibration energy harvester using a combined nonlinearity: the magnetic nonlinearity induced by magnetic force and the piecewise-linearity produced by mechanical impact. With extra stable states compared to other multi-stable harvesters, the quin-stable harvester can distribute its potential energy more uniformly, which provides shallower potential wells and results in lower excitation threshold for interwell motion. The mathematical model of this quin-stable harvester is derived and its equivalent piecewise-nonlinear restoring force is measured in the experiment and identified as piecewise polynomials. Numerical simulations and experimental verifications are performed in different levels of sinusoid excitation ranging from 1 to 25 Hz. The results demonstrate that, with lower potential barriers compared with tri-stable counterpart, the quin-stable arrangement can escape potential wells more easily for doing high-energy interwell motion over a wider band of frequencies. Moreover, by utilizing the mechanical stoppers, this harvester can produce significant output voltage under small tip deflections, which results in a high power density and is especially suitable for a compact MEMS approach.

In order to make a piezoelectric vibration energy harvester collect more energy on a broader frequency range, nonlinearity is introduced into the system, allowing the harvester to produce multiple steady states and deflecting the frequency response curve. However, the harvester can easily maintain intra-well motion rather than inter-well motion, which seriously affects its efficiency. The aim of this paper is to analyze how to take full advantage of the nonlinear characteristics to widen the bandwidth of the piezoelectric vibration energy harvester and obtain more energy. The influence of the inter-permanent magnet torque on the bending of the piezoelectric cantilever beam is considered in the theoretical modeling. The approximate analytical solutions of the primary and 1/3 subharmonic resonance of the harvester are obtained by using the complex dynamic frequency (CDF) method so as to compare the energy acquisition effect of the primary resonance and subharmonic resonance, determine the generation conditions of subharmonic resonance, and analyze the effect of primary resonance and subharmonic resonance on broadening the bandwidth of the harvester under different external excitations. The results show that the torque significantly affects the equilibrium point and piezoelectric output of the harvester. The effective frequency band of the bistable nonlinear energy harvester is 270% wider than that of the linear harvester, and the 1/3 subharmonic resonance broadens the band another 92% so that the energy harvester can obtain more than 0.1 mW in the frequency range of 18 Hz. Therefore, it is necessary to consider the influence of torque when modeling. The introduction of nonlinearity can broaden the frequency band of the harvester when it is in primary resonance, and the subharmonic resonance can make the harvester obtain more energy in the global frequency range.