Shoshani O, Shaw S W, Dykman M I
Ben-Gurion University of the Negev, Beer-Sheva, 8410501, Israel.
Florida Institute of Technology, Melbourne, FL 32901, USA.
Sci Rep. 2017 Dec 22;7(1):18091. doi: 10.1038/s41598-017-17184-6.
Because of the small size of nanomechanical systems, their vibrations become nonlinear already for small amplitudes. Many nontrivial aspects of the vibration dynamics arise from the coexistence of several nonlinearly coupled modes. We show that such coupling can lead to anomalous decay of the modes where they go through nonlinear resonance, so that their amplitude-dependent frequencies become commensurate. We demonstrate the possibility of a strongly nonmonotonic dependence of the decay rate on the amplitude if one of the modes serves as a thermal reservoir for another mode. Where the decay of both modes is slow compared to the rate of resonant energy exchange, the decay is accompanied by amplitude oscillations. Depending on the initial conditions, with increasing time it can display an extremely sharp or a comparatively smooth crossover between different regimes. The results provide insight into recent experimental results by several groups and suggest new ways of characterizing and controlling nanomechanical systems.
由于纳米机械系统尺寸小，其振动在小振幅时就会变为非线性。振动动力学的许多重要方面源于几种非线性耦合模式的共存。我们表明，这种耦合会导致模式在经历非线性共振时出现异常衰减，从而使它们与振幅相关的频率变得可公度。我们证明，如果其中一个模式作为另一个模式的热库，衰减率可能会对振幅呈现强烈的非单调依赖。当两个模式的衰减与共振能量交换速率相比都较慢时，衰减会伴随着振幅振荡。根据初始条件，随着时间增加，它可以在不同状态之间呈现极其尖锐或相对平滑的转变。这些结果为几个研究小组最近的实验结果提供了见解，并提出了表征和控制纳米机械系统的新方法。
