Investigation of an Electrically Driven Microelectromechanical System Resonator Under Mechanical Shock Effect with Quintic Nonlinearity

Mohamed Emad Abdelraouf (), Ahmed Elsaid, Kai Morino, Waheed K. Zahra and Ali Kandil ()
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Mohamed Emad Abdelraouf: Department of Mathematics, Institute of Basic and Applied Sciences, Egypt-Japan University of Science and Technology (E-JUST), New Borg El-Arab 21934, Egypt
Ahmed Elsaid: Department of Mathematics, Institute of Basic and Applied Sciences, Egypt-Japan University of Science and Technology (E-JUST), New Borg El-Arab 21934, Egypt
Kai Morino: Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka 816-8580, Japan
Waheed K. Zahra: Department of Mathematics, Institute of Basic and Applied Sciences, Egypt-Japan University of Science and Technology (E-JUST), New Borg El-Arab 21934, Egypt
Ali Kandil: Department of Mathematics, Institute of Basic and Applied Sciences, Egypt-Japan University of Science and Technology (E-JUST), New Borg El-Arab 21934, Egypt

Mathematics, 2025, vol. 13, issue 23, 1-24

Abstract: In a variety of applications, including signal processing, clock referencing, sensing, and others, microelectromechanical systems (MEMS) have been shown to be effective and broadly used. This study explores the dynamical response of a nonlinear MEMS resonator when subjected to a sudden mechanical shock under electrical excitation in the presence of quintic nonlinearity. The method of multiple scales (MMS) is utilized to construct the analytical formulas for analyzing the amplitude and phase response during primary resonance conditions. The analytical results are verified and compared with numerical simulations performed using the fourth-order Runge–Kutta method. Additionally, a parametric analysis is performed to examine the effect of different shock values on the resonator’s response and stability utilizing the Jacobian matrix. The agreement between analytical and numerical approaches proves MMS’s effectiveness in analyzing the shock impact on the MEMS resonator. The results provide valuable knowledge about the response and stability of MEMS resonators under mechanical shock, which is crucial for robust design in challenging conditions.

Keywords: MEMS resonator; mechanical shock; frequency response; shock response; method of multiple scales; quintic nonlinearity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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