Periodic solutions and the avoidance of pull-in instability in nonautonomous microelectromechanical systems
Kadyrov S. Kashkynbayev A. Skrzypacz P. Kaloudis K. Bountis A.
December 2021John Wiley and Sons Ltd
Mathematical Methods in the Applied Sciences
2021#44Issue 1814556 - 14568 pp.
We study periodic solutions of a one-degree of freedom microelectromechanical system (MEMS) with a parallel-plate capacitor under T-periodic electrostatic forcing. We obtain analytical results concerning the existence of T-periodic solutions of the problem in the case of arbitrary nonlinear restoring force, as well as when the moving plate is attached to a spring fabricated using graphene. We then demonstrate numerically on a T-periodic Poincaré map of the flow that these solutions are generally locally stable with large “islands” of initial conditions around them, within which the pull-in stability is completely avoided. We also demonstrate graphically on the Poincaré map that stable periodic solutions with higher period nT, n > 1 also exist, for wide parameter ranges, with large “islands” of bounded motion around them, within which all initial conditions avoid the pull-in instability, thus helping us significantly increase the domain of safe operation of these MEMS models.
dynamical systems , forced graphene oscillator , MEMS , pull-in
Text of the article Перейти на текст статьи
Suleyman Demirel University, Kaskelen, Kazakhstan
School of Sciences and Humanities, Nazarbayev University, Nur-Sultan, Kazakhstan
Department of Mechanical and Aerospace Engineering, Nazarbayev University, Nur-Sultan, Kazakhstan
Department of Mathematics, University of Patras, Patras, Greece
Suleyman Demirel University
School of Sciences and Humanities
Department of Mechanical and Aerospace Engineering
Department of Mathematics
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026