A Variational Principle for a Nonlinear Oscillator Arising in the ‎Microelectromechanical System

Document Type : Research Paper


1 National Engineering Laboratory for Modern Silk, College of Textile and Engineering, Soochow University, Suzhou, China

2 School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, China

3 School of Science, Xi'an University of Architecture and Technology, Xi’an, China

4 School of Mathematical Sciences, Soochow University, Suzhou, China‎

5 Department of Mathematics, Government College University, Faisalabad, Pakistan

6 School of Science and Technology, Nazarbayev University, 53 Kabanbay Batyr Ave., Astana, 010000, Kazakhstan‎


A nonlinear oscillator arising in the microelectromechanical system is complex and it is difficult to obtain a variational principle. This paper begins with a wrong variational formulation and uses the semi-inverse method to obtain a genuine variational principle. Additionally, this paper gives simple formula for the fast frequency estimation of the nonlinear oscillator. Only simple calculation is needed to have a relatively high accuracy results when compared with the other methods.


Main Subjects

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