Prospects for Nonlinear Energy Harvesting Systems Designed Near the Elastic Stability Limit When Driven by Colored Noise

Abstract

Ambient vibration sources in many prime energy harvesting applications are characterized as having stochastic response with spectra concentrated at low frequencies and steadily reduced power density as frequency increases (colored noise). To overcome challenges in designing linear resonant systems for such inputs, nonlinear restoring potential shaping has become a popular means of extending a harvester's bandwidth downward towards the highest concentration of excitation energy available. Due to recent works which have individually probed by analysis, simulation, or experiment the opportunity for harvester restoring potential shaping near the elastic stability limit (buckling transition) to improve power generation in stochastic environments-in most cases focusing on postbuckled designs and in some cases arriving at conflicting conclusionswe seek to provide a consolidated and insightful investigation for energy harvester performance employing designs in this critical regime. Practical aspects drive the study and encourage evaluation of the role of asymmetries in restoring potential forms. New analytical, numerical, and experimental investigations are conducted and compared to rigorously assess the opportunities and reach well-informed conclusions. Weakly bistable systems are shown to potentially provide minor performance benefits but necessitate a priori knowledge of the excitation environment and careful avoidance of asymmetries. It is found that a system designed as close to the elastic stability limit as possible, without passing the buckling transition, may be the wiser solution to energy harvesting in colored noise environments.

A systematic path to non-Markovian dynamics: new response probability density function evolution equations under Gaussian coloured noise excitation

“…Remark 3.1: The rationale behind the use of Volterra-Taylor series (31) for expanding stochastic functionals (30), is, in essence, to decompose the effects of nonlinearities into mean effects, and fluctuation effects. The first part (being nonlinear and nonlocal) is included in the final equation without any approximation, through the term…”

“…Formulating genFPK equations was initiated in the 70's by the works of van Kampen [23], Fox [24] and Hänggi [25], developed further in the 80's, [22,[26][27][28][29] (see also the seminal survey work of Hänggi and Jung [8]), and has been employed in many applications up to now. Examples of recent works applying genFPK equations to various disciplines are: [30] in energy harvesting, [31] in sensors design, [32] in laser technology, [33] in stochastic resonance, [16,34,35] in ecosystems, and [11,36,37] in medical science.…”

Method for controlling vibration by exploiting piecewise-linear nonlinearity in energy harvesters

“…Thus, traditional linear energy harvesters are usually limited to very narrow frequency ranges. In order to broaden the frequency bandwidth for effective energy harvesting, different techniques such as nonlinear energy harvesting [2,[18][19][20][21][22][23][24][25][26][27], array-harvester systems [28,29], and frequencytunable systems [30] have been developed so the harvester can accommodate a broader frequency range. Each technique has its own advantages and disadvantages.…”

“…For instance, the array-harvester design can harvest the vibration energy over resonant frequencies of each linear system; however, the system set-up and the corresponding electronic configuration are complex, which makes the utilization very challenging [5]. Nonlinear energy harvesters [2,[18][19][20][21][22][23][24][25][26][27], which are commonly used in piezoelectric and electromagnetic generators, can broaden the effective frequency bandwidth by exploiting geometric and material nonlinearities; however, these nonlinear techniques are not as efficient as linear energy harvesters at resonance.…”

Nonlinear Hybrid Piezoelectric and Electromagnetic Energy Harvesting Driven by Colored Excitation

“…Nevertheless, many environmental excitations have most of their energy trapped within a narrow bandwidth, which is also a characteristic of colored excitation. As a result, a narrow-band (colored) excitation could be more representative of key ambient vibration sources [27][28][29].…”