On the dynamic pull-in instability in a mass-spring model of electrostatically actuated MEMS devices

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• 作者：Gilberto Flores ^{gfg@mym.iimas.unam.mx}
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：262
• 期：6
• 页码：3597-3609
• 全文大小：270 K
• 卷排序：262

文摘

In this work we study the mass-spring systemequation(1)x¨+αx˙+x=−λ(1+x)2, which is a simplified model for an electrostatically actuated MEMS device. The static pull-in value is λ⁎=427, which corresponds to the largest value of λ   for which there exists at least one stationary solution. For λ>λ⁎λ>λ⁎ there are no stationary solutions and x(t)x(t) achieves the value −1 in finite time: touchdown   occurs. The maximal displacement achieved by a stationary solution, known as the pull-in distance, is equal to −13 in this model. Assuming that the motion starts from rest, we establish the existence of a dynamic pull-in value λd⁎(α)∈(0,λ⁎), defined for α∈[0,∞)α∈[0,∞), which is a threshold in the sense that x(t)x(t) approaches a stable stationary solution as t→∞t→∞ for 0<λ<λd⁎(α), while touchdown occurs for λ>λd⁎(α). This dynamic pull-in value is a continuous, strictly increasing function of α   and limα→∞⁡λd⁎(α)=λ⁎. A similar result is obtained for initial conditions of the form x(0)∈(−13,1), x˙(0)=0.