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Vibrational resonances in driven oscillators with position-dependent mass.

T O Roy-Layinde1, U E Vincent2,3, S A Abolade4

  • 1Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Ogun State, Nigeria.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
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This study extends vibrational resonance (VR) to systems with position-dependent mass (PDM). PDM effects can enhance VR, offering new avenues for optimizing device efficiency.

Keywords:
Duffing oscillatornonlinear systemsposition-dependent massstochastic resonancevibrational resonance

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Area of Science:

  • Nonlinear dynamics
  • Complex systems physics
  • Oscillatory phenomena

Background:

  • Vibrational resonance (VR) is a well-studied phenomenon in systems with constant mass.
  • Previous research has been limited to systems where mass remains unchanged.
  • Extending VR to systems with varying mass is a significant theoretical challenge.

Purpose of the Study:

  • To extend the vibrational resonance (VR) formalism to systems with position-dependent mass (PDM).
  • To analyze the vibrational resonance phenomena in generalized classical nonlinear oscillators with PDM.
  • To explore the potential of PDM effects in enhancing VR for device applications.

Main Methods:

  • Development of a theoretical framework to determine the response amplitude of PDM systems.
  • Analysis of vibrational resonance phenomena in nonlinear oscillators with position-dependent mass.
  • Examination of conditions for resonance occurrence in PDM systems.

Main Results:

  • The study successfully extends the VR formalism to systems with position-dependent mass (PDM).
  • Conditions for the occurrence of resonances in PDM systems were established.
  • It was shown that PDM can play both inductive and contributory roles in VR phenomena.

Conclusions:

  • Position-dependent mass (PDM) effects can be advantageously utilized to maximize the efficiency of devices operating in vibrational resonance (VR) modes.
  • The findings suggest new research directions for investigating VR in a broader class of PDM systems.
  • This work opens up possibilities for novel applications of VR in engineering and physics.