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

Abstract

PurposeThe 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/approachThis 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.FindingsThe semi-inverse method is a good mathematical tool to the search for a genuine fractal variational formulation for the N/MEMS system.Research limitations/implicationsThe 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 implicationsThe variational principle can be used for variational-based finite element methods and energy-based analytical methods.Originality/valueThe 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.