Periodic Oscillations in MEMS under Squeeze Film Damping Force
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 dam...
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Wiley
2022-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/1498981 |
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| author | Juan Beron Andrés Rivera |
| author_facet | Juan Beron Andrés Rivera |
| author_sort | Juan Beron |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-92aafa75604a4393847d9b18ea4974fc |
| institution | Kabale University |
| issn | 1687-0042 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-92aafa75604a4393847d9b18ea4974fc2025-02-03T06:05:02ZengWileyJournal of Applied Mathematics1687-00422022-01-01202210.1155/2022/1498981Periodic Oscillations in MEMS under Squeeze Film Damping ForceJuan Beron0Andrés Rivera1Departamento de Ciencias Naturales y Matemáticas Pontificia Universidad Javeriana CaliDepartamento de Ciencias Naturales y Matemáticas Pontificia Universidad Javeriana CaliWe 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.http://dx.doi.org/10.1155/2022/1498981 |
| spellingShingle | Juan Beron Andrés Rivera Periodic Oscillations in MEMS under Squeeze Film Damping Force Journal of Applied Mathematics |
| title | Periodic Oscillations in MEMS under Squeeze Film Damping Force |
| title_full | Periodic Oscillations in MEMS under Squeeze Film Damping Force |
| title_fullStr | Periodic Oscillations in MEMS under Squeeze Film Damping Force |
| title_full_unstemmed | Periodic Oscillations in MEMS under Squeeze Film Damping Force |
| title_short | Periodic Oscillations in MEMS under Squeeze Film Damping Force |
| title_sort | periodic oscillations in mems under squeeze film damping force |
| url | http://dx.doi.org/10.1155/2022/1498981 |
| work_keys_str_mv | AT juanberon periodicoscillationsinmemsundersqueezefilmdampingforce AT andresrivera periodicoscillationsinmemsundersqueezefilmdampingforce |