Abstract In this paper, the nonlinear vibration of a size-dependent doubly clamped NEMS has been investigated based on the consistent couple-stress theory and Euler-Bernoulli beam theory. The impact of surface elasticity, dispersion Casimir force, and fringing field effect are considered in the nonlinear model. Here, the nanobeam is supposed to be under a single-side electrostatic actuation, which is a combination of DC and AC voltages. The governing differential equation of motion is derived using the extended Hamilton’s principle and discretized to a nonlinear ODE using Galerkin’s procedure. The multiple time scales method is applied to the reduced-order model in order to analytically obtain the nanobeam frequency–response curves under hard AC load. The influence of the small-scale parameter, Casimir force, and surface effect are investigated on both the static pull-in and the superharmonic resonance characteristics of the system. It is shown that the application of non-classical continuum theory effectively shifts the saddle-node bifurcation point’s loci to lower frequencies, and diminishes the maximum amplitude of the system response without changing the system stiffness. Moreover, it is concluded that the influence of surface energy on the system dynamic behavior depends on the value of DC voltage load. To validate the results obtained from perturbation analysis, the shooting method is schemed through numerical integration of the reduced-order model equation.

中文翻译：

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纳米结构对纳米束电容器超谐波共振特性的影响：分析方法

摘要 在本文中，基于一致耦合应力理论和欧拉-伯努利梁理论，研究了尺寸相关双钳位NEMS 的非线性振动。非线性模型考虑了表面弹性、色散卡西米尔力和边缘场效应的影响。在这里，纳米束应该受到单侧静电驱动，这是直流和交流电压的组合。运动的控制微分方程是使用扩展的哈密顿原理推导出来的，并使用伽辽金程序离散为非线性常微分方程。将多时间尺度方法应用于降阶模型，以便解析地获得硬交流负载下的纳米梁频率响应曲线。小尺度参数卡西米尔力的影响，和表面效应对系统的静态吸合和超谐波共振特性进行了研究。结果表明，非经典连续介质理论的应用有效地将鞍节点分岔点的轨迹移至较低频率，并在不改变系统刚度的情况下减小了系统响应的最大幅度。此外，还得出结论，表面能对系统动态行为的影响取决于直流电压负载的值。为了验证微扰分析的结果，通过对降阶模型方程进行数值积分，设计了射击方法。结果表明，非经典连续介质理论的应用有效地将鞍节点分岔点的轨迹移至较低频率，并在不改变系统刚度的情况下减小了系统响应的最大幅度。此外，还得出结论，表面能对系统动态行为的影响取决于直流电压负载的值。为了验证微扰分析的结果，通过对降阶模型方程进行数值积分，设计了射击方法。结果表明，非经典连续介质理论的应用有效地将鞍节点分岔点的轨迹移至较低频率，并在不改变系统刚度的情况下减小了系统响应的最大幅度。此外，还得出结论，表面能对系统动态行为的影响取决于直流电压负载的值。为了验证微扰分析的结果，通过对降阶模型方程进行数值积分，设计了射击方法。