A variational principle for a fractal nano/microelectromechanical (N/MEMS) system

• Published in: International journal of numerical methods for heat & fluid flow Vol. 33; no. 1; pp. 351 - 359
• Main Author: He, Chun-Hui
• Format: Journal Article
• Language: English
• Published: Bradford Emerald Publishing Limited 03-01-2023; Emerald Group Publishing Limited
• Subjects: Analytical methods; Finite element method; Fractals; Inverse method; Iterative methods; Mathematical analysis; Methods; Microelectromechanical systems; Numerical analysis; Numerical methods; Principles; Variational theory; Duffing oscillator; Euler–Lagrange equation; MEMS oscillator
• ISSN: 0961-5539; 1758-6585; 0961-5539
• DOI: 10.1108/HFF-03-2022-0191

Purpose
The variational principle views a complex problem in an energy way, it gives good physical understanding of an iteration method, and the variational-based numerical methods always have a conservation scheme with a fast convergent rate. The purpose of this paper is to establish a variational principle for a fractal nano/microelectromechanical (N/MEMS) system.
Design/methodology/approach
This paper begins with an approximate variational principle in literature for the studied problem, and a genuine variational principle is obtained by the semi-inverse method.
Findings
The semi-inverse method is a good mathematical tool to the search for a genuine fractal variational formulation for the N/MEMS system.
Research limitations/implications
The established variational principle can be used for both analytical and numerical analyses of the N/MEMS systems, and it can be extended to some more complex cases.
Practical implications
The variational principle can be used for variational-based finite element methods and energy-based analytical methods.
Originality/value
The new and genuine variational principle is obtained. This paper discovers the missing piece of the puzzle for the establishment of a variational principle from governing equations for a complex problem by the semi-inverse method. The new variational theory opens a new direction in fractal MEMS systems.