VARIATIONAL APPROACH TO MICRO-ELECTRO-MECHANICAL SYSTEMS

This paper presents a novel approach for formulating a variational principle tailored to microelectromechanical systems (MEMS) through the utilization of the semi-inverse method. The resulting variational principle is that of least action, which is of considerable significance. The newly presented variational principle has the potential to be applied in a number of advantageous ways. One of the primary applications of this approach is the determination of the pull-in voltage. The application of this principle allows for a more accurate and efficient determination of the pull-in voltage. This is of paramount importance for the optimal functioning and optimization of MEMS devices. The enhanced accuracy in determining the pull-in voltage enables more precise design and greater reliability of MEMS-based systems. Additionally, the enhanced computational efficiency allows for the saving of valuable time and resources during the design process. Furthermore, the paper addresses the topic of fractal MEMS and puts forth a novel approach to fractional differentiation based on two-scale fractal differentiation, which is anticipated to facilitate the discovery of new insights and optimization strategies for MEMS devices.