In this study, for the first time, we investigate the nonlocality superimposed to the size effects on the nonlinear dynamics of an electrically actuated single-walled carbon-nanotube-based resonator. We undertake two models to capture the nanostructure nonlocal size effects: the strain and the velocity gradient theories. We use a reduced-order model based on the differential quadrature method (DQM) to discretize the governing nonlinear equation of motion and acquire a discretized-parameter nonlinear model of the system. The structural nonlinear behavior of the system assuming both strain and velocity gradient theories is investigated using the discretized model. The results suggest that nonlocal and size effects should not be neglected because they improve the prediction of corresponding dynamic amplitudes and, most importantly, the critical resonant frequencies of such nanoresonators. Neglecting these effects may impose a considerable source of error, which can be amended using more accurate modeling techniques.

在这项研究中，我们第一次研究了非局部性，该非局部性与尺寸影响对电驱动单壁碳纳米管基谐振器的非线性动力学有影响。我们采用两个模型来捕获纳米结构的非局部尺寸效应：应变和速度梯度理论。我们使用基于微分正交方法（DQM）的降阶模型来离散化控制的运动非线性方程，并获得系统的离散化参数非线性模型。使用离散模型研究了同时假设应变和速度梯度理论的系统的结构非线性行为。结果表明，非局部效应和尺寸效应不可忽略，因为它们改善了相应动态幅度的预测，最重要的是，这种纳米谐振器的临界谐振频率。忽略这些影响可能会带来很大的误差源，可以使用更精确的建模技术对其进行修正。