Approximate Fokker–Planck–Kolmo-gorov equation analysis for asymmetric multistable energy harvesters excited by white noise

Abstract

Due to the broadband response characteristics at low levels of excitations, nonlinear multistable systems have garnered a great deal of attention in the area of energy harvesting. Moreover, various performance enhancement strategies of multistable harvesters have been proposed and discussed extensively for systems with perfectly symmetric potentials. However, it is very difficult or even impossible in practice to modulate a nonlinear system with completely symmetric potentials. Therefore, this paper investigates the stochastic response characteristics of asymmetric potential multistable harvesters excited by Gaussian white noise. Approximate Fokker–Planck–Kolmogorov equation for multistable harvester is provided, and solved by the method of detailed balance. Numerical simulations are carried out to characterize the probability distribution and power output of the response of the harvesters. Results indicate that the theoretical method could well predict the response probability distribution of the systems under white noise excitations. To be more specific, the probability distribution of velocity response at a given excitation level is not affected by the asymmetry of potentials, while the probability density function of displacement is very dependent on the shape of potentials. In terms of the power output, the numerical results agree well with the theoretical results. However, the error between numerical and theoretical results increases with the increase in the number of the steady states and the degree of asymmetry of the harvesters.

Multistable vibration energy harvesters: Principle, progress, and perspectives

“…They found that the number of stable equilibrium positions influences the trivial and nontrivial steady-state solutions. Wang et al [88] investigated stochastic characteristics of asymmetric MEHs and provided an approximate FPK equation. They found that at a constant noise intensity, the probability distribution of velocity response of the harvester is almost unaffected by the potential function shape.…”

Nonlinear Dynamic Response of Galfenol Cantilever Energy Harvester Considering Geometric Nonlinear with a Nonlinear Energy Sink

“…The harvested electric energy can power low-power online monitoring and sensing devices in practical engineering, such as vehicle tracking, structural health monitoring, environmental monitoring, intelligent building, and aerospace fields [1][2][3]. In the literature, several energy harvesting mechanisms have been introduced to transform such vibration energy into electricity, for instance, electrostatic [4,5], electromagnetic [6,7], piezoelectric [8][9][10][11][12], and magnetostrictive [13,14].…”

Probabilistic Response and Performance Predict of Nonlinear Vibration Energy Harvesting Systems Based on Partial Information

“…In addition, as another effective analytical tool of the stochastic system, the path integration procedure was also developed to analyze the probabilistic solution of nonlinear VEH systems [29][30][31]. In addition, Wang et al [32] obtained the probability density functions (PDFs) of asymmetric multistable energy harvesters by the principle of detailed balance that found the design of the asymmetric structure is more conducive to improving the energy harvesting performance relative to the symmetric case. From the above research results, it is not hard to see that those theoretical analysis methods are all established based on all the information of the stochastic model.…”