Nonlinear dynamics and performance analysis of modified snap-through vibration energy harvester with time-varying potential function

• Published in: Applied mathematics and mechanics 2022-02, Vol.43 (2), p.185-202
• Main Authors: Devarajan, K., Santhosh, B.
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Chaos theory; Classical Mechanics; Differential equations; Dynamical systems; Energy; Energy harvesting; Fluid- and Aerodynamics; Fokker-Planck equation; Harmonic excitation; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Monte Carlo simulation; Nonlinear dynamics; Partial Differential Equations; Performance enhancement; Probability density functions; Random excitation; Stochastic resonance; Vibration analysis; Wave power
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-022-2812-8

Vibration energy harvesting has emerged as a promising method to harvest energy for small-scale applications. Enhancing the performance of a vibration energy harvester (VEH) incorporating nonlinear techniques, for example, the snap-through VEH with geometric non-linearity, has gained attention in recent years. A conventional snap-through VEH is a bi-stable system with a time-invariant potential function, which was investigated extensively in the past. In this work, a modified snap-through VEH with a time-varying potential function subject to harmonic and random base excitations is investigated. Modified snap-through VEHs, such as the one considered in this study, are used in wave energy harvesters. However, the studies on their dynamics and energy harvesting under harmonic and random excitations are limited. The dynamics of the modified snap-through VEH is represented by a system of differential algebraic equations (DAEs), and the numerical schemes are proposed for its solutions. Under a harmonic excitation, the system exhibits periodic and chaotic motions, and the energy harvesting is superior compared with the conventional counterpart. The dynamics under a random excitation is investigated by the moment differential method and the numerical scheme based on the modified Euler-Maruyama method. The Fokker-Planck equation representing the dynamics is derived, and the marginal and joint probability density functions (PDFs) are obtained by the Monte Carlo simulation. The study shows that the modified snap-through oscillator based VEH performs better under both harmonic and random excitations. The dynamics of the system under stochastic resonance (SR) is investigated, and performance enhancement is observed. The results from this study will help in the development of adaptive VEH techniques in the future.