Parametric resonance is a type of nonlinear vibration phenomenon [1], [2] induced from the periodic modulation of at least one of the system parameters and has the potential to exhibit interesting higher order nonlinear behaviour [3]. Parametrically excited vibration energy harvesters have been previously shown to enhance both the power amplitude [4] and the frequency bandwidth [5] when compared to the conventional direct resonant approach. However, to practically activate the more profitable regions of parametric resonance, additional design mechanisms [6], [7] are required to overcome a critical initiation threshold amplitude. One route is to establish an autoparametric system where external direct excitation is internally coupled to parametric excitation [8]. For a coupled two degrees of freedom (DoF) oscillatory system, principal autoparametric resonance can be achieved when the natural frequency of the first DoF f1 is twice that of the second DoF f2 and the external excitation is in the vicinity of f1. This paper looks at combining rotary and translatory motion and use autoparametric resonance phenomena.

Some of the lingering challenges within the current paradigm of vibration energy harvesting (VEH) involve narrow operational frequency range and the inevitable non-resonant response from broadband noise excitations. Such VEHs are only suitable for limited applications with fixed sinusoidal vibration, and fail to capture a large spectrum of the real world vibration. Various arraying designs, frequency tuning schemes and nonlinear vibratory approaches have only yielded modest enhancements. To fundamentally address this, the paper proposes and explores the potentials in using highly nonlinear magnetic spring force to activate an autoparametric oscillator, in order to realize an inherently broadband resonant system. Analytical and numerical modelling illustrate that high spring nonlinearity derived from magnetic levitation helps to promote the 2:1 internal frequency matching required to activate parametric resonance. At the right internal parameters, the resulting system can intrinsically exhibit semi-resonant response regardless of the bandwidth of the input vibration, including broadband white noise excitation.