Synchronized Frequency Conversion in Nonlinear Lattices

Abstract eng:
We investigate energy transfer between frequencies in lattices of interacting magnets with defects. The nonlinear coupling between localized and extended lattice modes enables to convert energy between arbitrary frequencies (i.e., non related by integer ratios). In addition, in systems with multiple defects, this frequency conversion mechanism allows harvesting energy from several input frequencies in a synchronized manner. These results may inform the design of new vibration energy harvesting systems. Vibration energy harvesting systems are able to convert ambient vibrations into electric power and are receiving a lot of interest in recent years [1]. Regardless of the transduction mechanism (e.g., piezoelectric, electromechanic), these systems operate optimally at or close to resonance. However, ambient vibrations are in general broadband or composed of multiple frequencies, which render these devices unsuited in most practical situations. A possible way to solve this issue is to introduce a frequency conversion mechanism in the system in order to match the spectrum of the excitation with the resonance frequency of the transducer. Typical uses of nonlinearity for frequency conversion are based on the phenomena of harmonic generation [2] and parametric down conversion [3]. In these mechanisms, the energy transfer occurs at a frequency that is an integer multiple or submultiple of the excitation frequency, limiting the applicability of these techniques. In this work, we demonstrate a frequency conversion mechanism in lattices of interacting magnets with mass defects that transfers energy between arbitrary frequencies, i.e., without being necessarily related by integer ratios. To illustrate this behavior we consider two cases: a lattice with a single defect [Fig. 1(a)] and a lattice containing two defects [Fig. 1(b)]. The linear spectrum of these lattices is composed of two types of modes: extended modes, which are responsible for the propagation of energy in the lattice; and defect modes, which are localized around the defect. Localized and extended modes represent respectively the inputs and outputs of our system. Due to the hardening nonlinearity of the magnetic potential [5], when the defect mode is excited harmonically at a frequency close to its resonance frequency, the mode undergoes hysteretic cycles in which the mode pumps the input energy to the chain [5]. This results in a modulation of the localized mode amplitude that creates an energy transfer from the localized modes to the extended modes. (b)

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