Broadband energy harvesting from parametric vibrations of a class of nonlinear Mathieu systems

Abstract

The nonlinear dynamics of the Mathieu equation with the inclusion of a cubic stiffness component is considered for broadband vibration energy harvesting. The results of numerical integration are compared with the corresponding solution of a regular Duffing oscillator which is widely used to model nonlinear energy harvesting. The use of Duffing oscillators has shown direct correspondence between the effective frequency range of the associated hysteretic phenomenon and the value of the nonlinearity coefficient. A broadband energy harvester requires strong nonlinearity, especially for high frequencies of interest. This letter demonstrates that the effectiveness of parametrically excited systems is not constrained by the same requirement. Based on this, it is suggested that parametrically excited systems can be a robust means of broadband vibration harvesting.