Periodic Oscillations in MEMS under Squeeze Film Damping Force

Juan Beron and Andrés Rivera

Journal of Applied Mathematics, 2022, vol. 2022, issue 1

Abstract: We provide sufficient conditions for the existence of periodic solutions for an idealized electrostatic actuator modeled by the Liénard‐type equation x¨+FDx,ẋ+x=βV2t/1−x2,x∈−∞,1 with β ∈ ℝ+, V∈Cℝ/Tℤ, and FDx,ẋ=κẋ/1−x3, κ ∈ ℝ+ (called squeeze film damping force), or FDx,ẋ=cẋ, c ∈ ℝ+ (called linear damping force). If FD 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 FD 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.

Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2022/1498981

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2022:y:2022:i:1:n:1498981

Access Statistics for this article

More articles in Journal of Applied Mathematics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().