Yousuf S M Enamul Hoque, Shaw Steven W, Feng Philip X-L
Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL, 32611, USA.
Department of Mechanical and Civil Engineering, Florida Institute of Technology, Melbourne, FL, 32901, USA.
Microsyst Nanoeng. 2024 Dec 27;10(1):206. doi: 10.1038/s41378-024-00844-9.
Nanoelectromechanical systems (NEMS) incorporating atomic or molecular layer van der Waals materials can support multimode resonances and exotic nonlinear dynamics. Here we investigate nonlinear coupling of closely spaced modes in a bilayer (2L) molybdenum disulfide (MoS) nanoelectromechanical resonator. We model the response from a drumhead resonator using equations of two resonant modes with a dispersive coupling term to describe the vibration induced frequency shifts that result from the induced change in tension. We employ method of averaging to solve the equations of coupled modes and extract an expression for the nonlinear coupling coefficient (λ) in closed form. Undriven thermomechanical noise spectral measurements are used to calibrate the vibration amplitude of mode 2 (a) in the displacement domain. We drive mode 2 near its natural frequency and measure the shifted resonance frequency of mode 1 (f) resulting from the dispersive coupling. Our model yields λ = 0.027 ± 0.005 pm · μs from thermomechanical noise measurement of mode 1. Our model also captures an anomalous frequency shift of the undriven mode 1 due to nonlinear coupling to the driven mode 2 mediated by large dynamic tension. This study provides a direct means to quantifying λ by measuring the thermomechanical noise in NEMS and will be valuable for understanding nonlinear mode coupling in emerging resonant systems.
包含原子或分子层范德华材料的纳米机电系统（NEMS）能够支持多模共振和奇异的非线性动力学。在此，我们研究双层（2L）二硫化钼（MoS）纳米机电谐振器中紧密间隔模式的非线性耦合。我们使用具有色散耦合项的两个共振模式方程对鼓面谐振器的响应进行建模，以描述由张力变化引起的振动诱导频率偏移。我们采用平均法求解耦合模式方程，并以封闭形式提取非线性耦合系数（λ）的表达式。未驱动的热机械噪声谱测量用于在位移域中校准模式2（a）的振动幅度。我们在模式2的固有频率附近驱动它，并测量由色散耦合导致的模式1（f）的共振频率偏移。通过对模式1的热机械噪声测量，我们的模型得出λ = 0.027±0.005 pm·μs。我们的模型还捕捉到了未驱动模式1由于与由大动态张力介导的驱动模式2的非线性耦合而产生的异常频率偏移。这项研究提供了一种通过测量NEMS中的热机械噪声来量化λ的直接方法，对于理解新兴共振系统中的非线性模式耦合将具有重要价值。
