Abstract

Internal resonance is a typical nonlinear phenomenon associated usually with double jumps, two peaks bending to the left and the right respectively in amplitude-frequency responses. The presentation begins with two cases in which 1:2 internal resonance results in the change of hardening and softening characteristics in the amplitude-frequency responses. One case is a pipe conveying fluid flowing in the supercritical speed, and the analysis is based on a discretized model. The other case is coupled cantilevers subjected to magnetic interaction, and the analysis is based on a distributed model. In both cases, with the increase or the decrease of a parameter, multi-scale analysis reveals that double jumps evolve from a jump with softening characteristic and disappear as a jump with hardening characteristic, and the analytical outcomes are supported by numerical simulations. Double jumps with internal resonance may be a possible mechanism to enhance energy harvesting by broadening the harvester working frequency bands. An electromagnetic device with snap-through nonlinearity is proposed as an archetype of an internal resonance energy harvester with double jumps in the amplitude-frequency responses derived from the method of multiple scales. To show the effectiveness, the averaged root-mean-square output voltages are calculated under four kinds of noses, namely, the Gaussian white noise, the colored noise defined by a second-order filter, the narrow-band noise, and exponentially correlated noise. Finally, an L-shaped cantilevered structure laminated with a piezoelectric patch and augmented with frequency tuning magnets is treated analytically, numerically and experimentally. All these works demonstrate that the internal resonance increases the opening bandwidth and the output electricity.