Resonance response interaction without internal resonance in vibratory energy harvesting

Resonance response interaction in nonlinear multiple degrees of freedom vibration systems has always involved internal resonance. In this article, bubble shaped response curve is uncovered without pre-designated resonances relationship that is a necessary condition for internal resonance. The objective of this article is twofold: first to explore the connection between the resonance response interaction and bubble shaped response curve that may appear in the forced response of a nonlinear magnetoelectric coupled system; and, second, to exploit resonance response interaction to enhance the vibratory energy harvesting bandwidth. A nonlinear magnetoelectric oscillator coupled linearly to an additional oscillator is used to demonstrate the phenomena and the enhanced performance. The lateral springs could produce the geometrical nonlinear stiffness and its stiffness to adjust the two resonance responses such that the bubble shaped response curve appears in the power-frequency response plot. The method of harmonic balance is well established method for the analysis of such the power-frequency response. The results are also validated by some numerical work. The power-frequency response curves are generated for distinct harvesting mass, manifesting the resonance response interaction could increase the bandwidth and output power. At last, the resonance response interaction designed energy harvesting from Gaussian white noise excitation is numerically addressed to illustrate positive effects of geometrical nonlinearity.