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)’.

中文翻译：

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具有位置相关质量的驱动振荡器中的振动共振

振动共振 (VR) 现象自引入以来的二十年来受到了广泛的研究关注。然而，获得的广泛的理论和实验结果仅限于具有恒定质量的系统中的 VR。我们现在将 VR 形式扩展到包含具有位置依赖质量 (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。通过开发确定 PDM 系统响应幅度的理论框架，我们检查和分析了它们的 VR 现象a，获得了共振发生的条件，表明 PDM 所起的作用可以是诱导性和贡献性的，并表明 PDM 效应可以有效地探索以最大限度地提高在 VR 模式下运行的设备的效率。我们的分析为在一般 PDM 系统中研究 VR 提出了新的方向。本文是主题问题“驱动非线性系统中的振动和随机共振（第 1 部分）”的一部分。