Electrostatic actuation is one of the most commonly used methods for excitation and measurement in micro and nanoscale resonators. In the dynamical behavior analyses of such systems, the resonating beam is often assumed to be a perfect conductor. In this paper, the effect of electrical resistivity on the vibrational response of these systems, including the natural frequency and damping, is investigated. The governing coupled nonlinear partial differential equations of motion are derived and a new finite element method formulation is presented by developing a new electromechanical element. The numerical natural frequencies are compared with experimental measurements and the achieved correlation is better than that in the prior studies. Results indicate that there is a jump in the frequency and damping of the system at a critical resistivity. As the system size decreases and the applied voltage approaches the pull-in voltage, the electrical resistivity completely dominates the response nature of the system. An experiment is also conducted, and good agreement with the theory is observed regarding the effect of electrical resistivity.

静电激励是在微米和纳米级谐振器中进行激励和测量的最常用方法之一。在此类系统的动力学行为分析中，通常将共振束假定为理想导体。本文研究了电阻率对这些系统的振动响应的影响，包括固有频率和阻尼。推导了控制耦合的非线性偏微分运动方程，并通过开发新的机电元件，提出了新的有限元方法公式。将数值固有频率与实验测量值进行比较，并且所获得的相关性优于先前的研究。结果表明，在临界电阻率下，系统的频率和阻尼都有跳跃。随着系统尺寸的减小以及所施加的电压接近引入电压，电阻率将完全主导系统的响应特性。还进行了实验，并且观察到与电阻率的影响理论相符。