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Vibrational resonances in driven oscillators with position-dependent mass

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<mark>Journal publication date</mark>8/03/2021
<mark>Journal</mark>Philosophical Transactions of the Royal Society of London A
Issue number2192
Number of pages23
Pages (from-to)1-23
Publication StatusPublished
Early online date18/01/21
<mark>Original language</mark>English


The vibrational resonance (VR) phenomenon has received a great deal of research attention over the two decades since its introduction. The wide range of theoretical and experimental results obtained has, however, been confined to VR in systems with constant mass. We now extend the VR formalism to encompass systems with position-dependent mass (PDM).We consider a generalized classical counterpart of the quantum mechanical nonlinear oscillator with PDM. By developing a theoretical framework fordetermining the response amplitude of PDMsystems, we examine and analyse their VR phenomenona, obtain conditions for the occurrence of resonances, show that the role played by PDM can be both inductive and contributory, and suggest that PDM effects could usefully be explored to maximise the efficiency of devices being operated in VRmodes. Our analysis suggests new directions for the investigation of VR in a general class of PDM systems.

Bibliographic note

Part of a Theme Issue on "Vibrational and Stochastic Resonance in Driven Nonlinear Systems".