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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1687-0042 |