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

Abstract

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.

Citation

He, C.-H. (2023), "A variational principle for a fractal nano/microelectromechanical (N/MEMS) system", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 1, pp. 351-359. https://doi.org/10.1108/HFF-03-2022-0191