Bistable Harvester Research Articles

Wideband energy harvesting using a combination of an optimized synchronous electric charge extraction circuit and a bistable harvester

The challenge of variable vibration frequencies for energy harvesting calls for the development of wideband energy harvesters. Bistability has been proven to be a potential solution. Optimization of the energy extraction is another important objective for energy harvesting. Nonlinear synchronized switching techniques have demonstrated some of the best performances. This paper presents a novel energy harvesting solution which combines these two techniques: the OSECE (optimized synchronous electric charge extraction) technique is used along with a BSM (buckled-spring–mass) bistable generator to achieve wideband energy harvesting. The effect of the electromechanical coupling coefficient on the harvested power for the bistable harvester with the nonlinear energy extraction technique is discussed for the first time. The performances of the proposed solution for different levels of electromechanical coupling coefficients in the cases of chirp and noise excitations are compared against the performances of the bistable harvester with the standard technique. It is shown that the OSECE technique is a much better option for wideband energy harvesting than the standard circuit. Moreover, the harvested energy is drastically increased for all excitations in the case of low electromechanical coupling coefficients. When the electromechanical coupling coefficient is high, the performance of the OSECE technique is not as good as the standard circuit for forward sweeps, but superior for the reverse sweep and band-limited noise cases. However, considering that real excitation signals are more similar to noise signals, the OSECE technique enhances the performance.

Bistable energy harvesting enhancement with an auxiliary linear oscillator

Recent work has indicated that linear vibrational energy harvesters with an appended degree-of-freedom (DOF) may be advantageous for introducing new dynamic forms to extend the operational bandwidth. Given the additional interest in bistable harvester designs, which exhibit a propitious snap through effect from one stable state to the other, it is a logical extension to explore the influence of an added DOF to a bistable system. However, bistable snap through is not a resonant phenomenon, which tempers the presumption that the dynamics induced by an additional DOF on bistable designs would inherently be beneficial as for linear systems. This paper presents two analytical formulations to assess the fundamental and superharmonic steady-state dynamics of an excited bistable energy harvester to which is attached an auxiliary linear oscillator. From an energy harvesting perspective, the model predicts that the additional linear DOF uniformly amplifies the bistable harvester response magnitude and generated power for excitation frequencies less than the attachment’s resonance while improved power density spans a bandwidth below this frequency. Analyses predict bandwidths having co-existent responses composed of a unique proportion of fundamental and superharmonic dynamics. Experiments validate key analytical predictions and observe the ability for the coupled system to develop an advantageous multi-harmonic interwell response when the initial conditions are insufficient for continuous high-energy orbit at the excitation frequency. Overall, the addition of an auxiliary linear oscillator to a bistable harvester is found to be an effective means of enhancing the energy harvesting performance and robustness.

Concise and high-fidelity predictive criteria for maximizing performance and robustness of bistable energy harvesters

We employ an analytical model of a harmonically excited bistable vibration energy harvester to determine criteria governing continuous high-energy orbit (HEO) dynamics that maximize harvesting performance. Derivation of the criteria stems from previously unexplored dynamic relationships predicted by the model indicating critical conditions for HEO; experimental evidence of the phenomenon is provided as validation. The criteria are vastly more concise than existing HEO prediction methodology and can more accurately delineate HEO boundaries. This research addresses an essential need to create effective tools for high performance and robust bistable harvester design.

Harmonic balance analysis of the bistable piezoelectric inertial generator

This paper applies the method of Harmonic Balance to analytically predict the existence, stability, and influence of parameter variations on the intrawell and interwell oscillations of bistable piezoelectric inertial generator. Existing work on the bistable piezoelectric harvester in the presence of varying harmonic environmental loading has been relegated to simulation and experimental analyses. Furthermore, linear piezoelectric behavior and linear damping has always been presumed. This paper improves upon an existing model for the bistable piezoelectric harvester by incorporating nonlinear dissipation and cubic softening influences in the electroelastic laminates before applying analytical methods. A framework for theoretically predicting empirical observations, such as optimal impedance loads for steady-state motions, is provided as well as other dynamic considerations such as potential well escape phenomena.

On intentional introduction of stiffness nonlinearities for energy harvesting under white Gaussian excitations

A significant body of the open literature on vibratory energy harvesting is currently focused on the concept of purposeful inclusion of stiffness nonlinearities for broadband transduction. When compared to their linear resonant counterparts, nonlinear energy harvesters have a wider steady-state frequency bandwidth, leading to the idea that they can be utilized to improve performance especially in random and non-stationary vibratory environments. To further investigate this common belief, this paper studies the response of vibratory energy harvesters to white Gaussian excitations. Both mono- and bi-stable piezoelectric Duffing-type harvesters are considered. The Fokker–Plank–Kolmogorov equation governing the evolution of the system’s transition probability density function is formulated and used to generate the moment differential equations governing the response statistics. The moment equations are then closed using a fourth-order cumulant-neglect closure scheme and the relevant steady-state response statistics are obtained. It is demonstrated that the energy harvester’s time constant ratio, i.e., the ratio between the nominal period of the mechanical subsystem and the time constant of the harvesting circuit, plays a critical role in characterizing the performance of nonlinear harvesters in a random environment. When the time constant ratio is large, stiffness-type nonlinearities have very little influence on the voltage response. In such a case, no matter how the potential function of the harvester is altered, it does not affect the average output power of the device. When the time constant ratio is small, the influence of the nonlinearity on the voltage output becomes more prevalent. In this case, a Duffing-type mono-stable harvester can never outperform its linear counterpart. A bi-stable harvester, on the other hand, can outperform a linear harvester only when it is designed with the proper potential energy function based on the known noise intensity of the excitation. Such conclusions hold for harvesters with nonlinearities appearing in the restoring force.

Relative performance of a vibratory energy harvester in mono- and bi-stable potentials

Motivated by the need for broadband vibratory energy harvesting, many research studies have recently proposed energy harvesters with nonlinear characteristics. Based on the shape of their potential function, such devices are classified as either mono- or bi-stable energy harvesters. This paper aims to investigate the relative performance of these two classes under similar excitations and electric loading conditions. To achieve this goal, an energy harvester consisting of a clamped–clamped piezoelectric beam bi-morph is considered. The shape of the harvester's potential function is altered by applying a static compressive axial load at one end of the beam. This permits operation in the mono-stable (pre-buckling) and bi-stable (post-buckling) configurations. For the purpose of performance comparison, the axial load is used to tune the harvester's oscillation frequencies around the static equilibria such that they have equal values in the mono- and bi-stable configurations. The harvester is subjected to harmonic base excitations of different magnitudes and a slowly varying frequency spanning a wide band around the tuned oscillation frequency. The output voltage measured across a purely resistive load is compared over the frequency range considered. Two cases are discussed; the first compares the performance when the bi-stable harvester has deep potential wells, while the second treats a bi-stable harvester with shallow wells. Both numerical and experimental results demonstrate the essential role that the potential shape plays in conjunction with the base acceleration to determine whether the bi-stable harvester can outperform the mono-stable one and for what range of frequencies. Results also illustrate that, for a bi-stable harvester with shallow potential wells, super-harmonic resonances can activate the inter-well dynamics even for a small base acceleration, thereby producing large voltages in the low frequency range.