Geometric potential in nano/microelectromechanical systems: Part I mathematical model

In recent decades, nano/microelectromechanical systems (N/MEMS) have garnered significant attention due to their appealing characteristics, such as compact size, batch fabrication capabilities, high reliability and low power consumption. However, these vibratory systems often present challenges, including zero conditions at the initial time, involving zero velocity and zero displacement, which complicates the solution process. Nonetheless, the theory of geometric potential offers insights into various phenomena in nanoscience and nanotechnology. In this paper, we implement the theory of geometric potential to develop an N/MEMS model. We then analyze the periodicity property of the nonlinear system using a novel method based on Sturm’s algorithm. Our analysis reveals that the model with zero initial conditions exhibits periodic solution under specific conditions on lumped parameter. Finally, we validate our findings by comparing them with numerically achieved results.