Roy-Layinde T O, Vincent U E, Abolade S A, Popoola O O, Laoye J A, McClintock P V E
Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Ogun State, Nigeria.
Department of Physical Sciences, Redeemer's University, P.M.B. 230 Ede, Nigeria.
Philos Trans A Math Phys Eng Sci. 2021 Mar 8;379(2192):20200227. doi: 10.1098/rsta.2020.0227. Epub 2021 Jan 18.
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 for determining the response amplitude of PDM systems, 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 maximize the efficiency of devices being operated in VR modes. Our analysis suggests new directions for the investigation of VR in a general class of PDM systems. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.
自振动共振（VR）现象被提出以来的二十年里，它受到了大量的研究关注。然而，所获得的广泛理论和实验结果仅限于质量恒定的系统中的VR。我们现在将VR形式主义扩展到包含质量与位置有关（PDM）的系统。我们考虑具有PDM的量子力学非线性振荡器的广义经典对应物。通过建立一个确定PDM系统响应幅度的理论框架，我们研究和分析它们的VR现象，获得共振发生的条件，表明PDM所起的作用既可以是诱导性的也可以是促成性的，并建议可以有效地探索PDM效应以最大化在VR模式下运行的设备的效率。我们的分析为一类一般的PDM系统中VR的研究提出了新的方向。本文是主题为“驱动非线性系统中的振动和随机共振（第1部分）”的一部分。
