In this paper, the size-dependent nonlinear vibration of an electrostatic nanobeam actuator is investigated based on the nonlocal strain gradient theory, incorporating surface effects. A comprehensive model regarding the von Karman geometrical nonlinearity, inter-molecular forces and both components of the electrostatic excitation (AC and DC) is proposed to explore the system behavior near the primary resonance. Utilizing Hamilton’s principle, the nonlinear equation of motion of the system is derived. The natural frequency and dynamic response of the system, comprising frequency and force response diagrams, are obtained analytically via multiple scales technique in conjunction with the differential quadrature method and validated through a numerical approach. The roles of the nonlocal and strain gradient parameters, surface elasticity, inter-molecular forces and quality factor on the system oscillations are examined. The acquired results unveiled that the size-dependent parameters can significantly displace the multi-valued portions and instability thresholds of the dynamical response. Furthermore, it is deduced that the surface effects induce the stiffness hardening of the nanobeam, whereas the inter-molecular forces impose the stiffness softening effect.

本文基于非局部应变梯度理论，结合表面效应，研究了静电纳米束致动器的尺寸依赖性非线性振动。提出了有关冯·卡曼几何非线性，分子间力以及静电激励的两个分量（交流和直流）的综合模型，以探索主共振附近的系统行为。利用汉密尔顿原理，推导了系统的非线性运动方程。系统的固有频率和动态响应（包括频率和力响应图）是通过多尺度技术结合差分正交方法以解析方式获得的，并通过数值方法进行了验证。非局部和应变梯度参数，表面弹性，考察了分子间的力和系统振荡的品质因数。获得的结果表明，与尺寸有关的参数可以显着取代动力响应的多值部分和不稳定性阈值。此外，推断出表面效应引起纳米束的刚度硬化，而分子间力施加刚度软化效应。