Nonlinear energy harvester with coupled Duffing oscillators

Abstract

Structural vibrations are very common in aerospace and mechanical engineering systems, where dynamic analysis of modern aerospace structures and industrial machines has become an indispensable step in their design. Suppression of unwanted vibrations and their exploitation for energy harvesting at the same time would be the most desirable scenario. The dynamical system presented in this communication is based on a discrete model of energy harvesting device realized in such a manner as to achieve both vibration suppression and harvesting of vibration energy by introducing the nonlinear energy sink concept. The mechanical model is formed as a two-degree of freedom nonlinear oscillator with an oscillating magnet and harmonic base excitation. The corresponding mathematical model is based on the system of nonlinear nonhomogeneous Duffing type differential equations. To explore complex dynamical behaviour of the presented model, periodic solutions and their bifurcations are found by using the incremental harmonic balance (IHB) and continuation methods. For the detection of unstable periodic orbits, the Floquet theory is applied and an interesting harmonic response of the presented nonlinear dynamical model is detected. The main advantage of the presented approach is its ability to obtain approximated periodic responses in terms of Fourier series and estimate the voltage output of an energy harvester for a system with strong nonlinearity. The accuracy of the presented methodology is verified by comparing the results obtained in this work with those obtained by a standard numerical integration method and results from the literature. Numerical examples show the effects of different physical parameters on amplitude-frequency, response amplitude - base amplitude and time response curves, where a qualitative change is explored and studied in detail. Presented theoretical results demonstrate that the proposed system has advanced performance in both system requirements - vibration suppression, and energy harvesting.