A numerical study of the pull-in instability in some free boundary models for MEMS

Gilberto Flores, Noel Smyth

Research output: Contribution to journalArticlepeer-review


In this work we numerically compute the bifurcation curve for stationary
solutions of the free boundary problem for MEMS in one space dimension. It
has a single turning point, as in the case of the small aspect ratio limit. We also
find a threshold for the existence of global in time solutions of the evolution
equation for the MEMS in the form of either a heat or a damped wave equation.
This threshold is what we term the dynamical pull-in value: it separates the
stable operating regime from the touchdown regime. The numerical calculations
show that the dynamical threshold values for the heat equation coincide with
the static values. For the damped wave equation the dynamical threshold values
are smaller than the static values. This result is in qualitative agreement with
those reported for the model of the MEMS based on a simplified mass-spring
system, as studied in the engineering literature. In the case of the damped wave
equation, we also show that the aspect ratio of the device is more important
than the inertia in the determination of the pull-in value.
Original languageEnglish
Pages (from-to)7962-7970
Number of pages17
JournalApplied mathematical modelling
Issue number17-18
Early online date6 May 2016
Publication statusPublished - Sep 2016


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