In this paper, we present a nonlinear electromagnetic energy harvesting device that has a broadly resonant response. The nonlinearity is generated by a particular arrangement of magnets in conjunction with an iron-cored stator. We show the resonant response of the system to both pure-tone excitation and narrow-band random excitation. In addition to the primary resonance, the superharmonic resonances of the harvester are also investigated and we show that the corresponding mechanical upconversion of the excitation frequency may be useful for energy harvesting. The harvester is modeled using a Duffing-type equation and the results are compared with the experimental data.

Control-based continuation is a recently developed approach for testing nonlinear dynamic systems in a controlled manner and exploring their dynamic features as system parameters are varied. In this paper, control-based continuation is adapted to follow the locus where system response and excitation are in quadrature, extracting the backbone curve of the underlying conservative system. The method is applied to a single-degree-of-freedom oscillator under base excitation, and the results are compared with the standard resonant-decay method

In this paper we present a systematic experimental study of two one-degree-of-freedom nonlinear devices using the newly introduced control-based continuation method of Sieber and Krauskopf. By considering hardening, softening and bistable spring characteristics, we demonstrate the versatility and power of the control-based continuation method for investigating nonlinear experiments. We show that, using this method, it is possible to track the stable orbits of the devices through a saddle-node bifurcation (fold) where they lose stability and continue them up to the resonance peak where they undergo a second saddle-node bifurcation. For the bistable case, a bifurcation diagram is produced that is strongly reminiscent of the bifurcation diagram produced using the classical harmonic balance solution. A detailed introduction to general continuation methods is included to enable implementation by other experimentalists.

We present a general method for systematically investigating the dynamics and bifurcations of a physical nonlinear experiment. In particular, we show how the odd-number limitation inherent in popular noninvasive control schemes, such as (Pyragas) time-delayed or washout-filtered feedback control, can be overcome for tracking equilibria or forced periodic orbits in experiments. To demonstrate the use of our noninvasive control, we trace out experimentally the resonance surface of a periodically forced mechanical nonlinear oscillator near the onset of instability, around two saddle-node bifurcations (folds) and a cusp bifurcation.