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- W2293933566 abstract "In this work we study the mass-spring system begin{equation} ddot x + alpha dot x + x = - frac{lambda} {(1+x)^{2}}, label{e:inertia} end{equation} which is a simplified model for an electrostatically actuated MEMS device. The static pull-in value is $lambda^{*}=frac{4}{27}$, which corresponds to the largest value of $lambda$ for which there exists at least one stationary solution. For $lambda > lambda^{*}$ there are no stationary solutions and $x(t)$ achieves the value $-1$ in finite time: {it touchdown} occurs. We establish the existence of a dynamic pull-in value $lambda_{d}^{*}(alpha) in (0, lambda^{*})$, defined for $alpha in [0,infty)$, which is a threshold in the sense that $x(t)$ approaches a stable stationary solution as $t to infty$ for $0 lambda_{d}^{*}(alpha)$. This dynamic pull-in value is a continuous, strictly increasing function of $alpha$ and $lim_{alphatoinfty} lambda_{d}^{*}(alpha)= lambda^{*}$." @default.
- W2293933566 created "2016-06-24" @default.
- W2293933566 creator A5035388138 @default.
- W2293933566 date "2016-02-19" @default.
- W2293933566 modified "2023-10-03" @default.
- W2293933566 title "On the dynamic pull-in instability in a mass-spring model of electrostatically actuated MEMS devices" @default.
- W2293933566 cites W1978201146 @default.
- W2293933566 hasPublicationYear "2016" @default.
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