Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774372 | Journal of Differential Equations | 2017 | 13 Pages |
Abstract
In this work we study the mass-spring system(1)x¨+αxË+x=âλ(1+x)2, which is a simplified model for an electrostatically actuated MEMS device. The static pull-in value is λâ=427, which corresponds to the largest value of λ for which there exists at least one stationary solution. For λ>λâ there are no stationary solutions and x(t) achieves the value â1 in finite time: touchdown occurs. The maximal displacement achieved by a stationary solution, known as the pull-in distance, is equal to â13 in this model. Assuming that the motion starts from rest, we establish the existence of a dynamic pull-in value λdâ(α)â(0,λâ), defined for αâ[0,â), which is a threshold in the sense that x(t) approaches a stable stationary solution as tââ for 0<λ<λdâ(α), while touchdown occurs for λ>λdâ(α). This dynamic pull-in value is a continuous, strictly increasing function of α and limαâââ¡Î»dâ(α)=λâ. A similar result is obtained for initial conditions of the form x(0)â(â13,1), xË(0)=0.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Gilberto Flores,