Periodic Oscillations in MEMS under Squeeze Film Damping Force. (2nd September 2022)

• Record Type: Journal Article
• Authors: Beron, Juan; Rivera, Andrés
• Other Names: Simoes Fernando Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2022(2022)
• Publication Date: 2022-09-02
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2022/1498981
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : We provide sufficient conditions for the existence of periodic solutions for an idealized electrostatic actuator modeled by the Liénard-type equation x ¨ + F D x, x ̇ + x = β V 2 t / 1 − x 2, x ∈ − ∞, 1 with β ∈ ℝ +, V ∈ C ℝ / T ℤ, and F D x, x ̇ = κ x ̇ / 1 − x 3, κ ∈ ℝ + (called squeeze film damping force), or F D x, x ̇ = c x ̇, c ∈ ℝ + (called linear damping force). If F D is of squeeze film type, we have proven that there exists at least two positive periodic solutions, one of them locally asymptotically stable. Meanwhile, if F D is a linear damping force, we have proven that there are only two positive periodic solutions. One is unstable, and the other is locally exponentially asymptotically stable with rate of decay of c / 2 . Our technique can be applied to a class of Liénard equations that model several microelectromechanical system devices, including the comb-drive finger model and torsional actuators.