Geodesic
Numerical study of mathematical models of micromechanics with periodic impulse action
Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 3, pp. 133-145

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We consider the results of the numerical study of mathematical models of two microelectromechanical systems (MEMS). We formulate matematical models as initial boundary value problems describing the cylindrical flexure of the elastic beam as a movable electrode under the action of a repetitive intensity impulse of the electrostatic field between the movable and fixed electrodes in a microgap. In the first problem, both ends of the beam are rigidly fixed, and in the second problem, we consider a cantilever beam. The range of the parameters is found for a model having two periodic solutions with periods of impulse interaction one of which is stable and the other is unstable.
Keywords: nonlinear oscillation, electrostatic attraction, method of lines, boundary value problem, continuation with respect to a parameter, nonuniqueness of solutions. 
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     author = {S. I. Fadeev and D. O. Pimanov},
     title = {Numerical study of mathematical models of micromechanics with periodic impulse action},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {133--145},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2013_16_3_a11/}
}
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S. I. Fadeev; D. O. Pimanov. Numerical study of mathematical models of micromechanics with periodic impulse action. Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 3, pp. 133-145. http://geodesic.mathdoc.fr/item/SJIM_2013_16_3_a11/