Geodesic
Researching of Periodic Solutions in a Mathematical Models of~Micromechanics with Pulsed Periodic Impact
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 3, pp. 122-140

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This paper considers results of the researching of nonlinear vibration in mathematical models of two microelectromechanical systems (MEMS). These models describe motion of moveable electrode in the micro-gap. The motion is due to the impact of repetitive pulse electrostatic field between the moveable and fixed electrodes. Thereby we formulate boundary value problems with periodicity conditions for the differential equation of motion of a point on plane and the hyperbolic equation. We found the range of parameters of models which consider a multiplicity of periodic solutions (two), one of which is stable and other — unstable.
Keywords: nonlinear vibration, electrostatic attraction, method of lines, boundary value problem, parameter continuation, multiplicity of solutions. 
@article{VNGU_2013_13_3_a11,
     author = {S. I. Fadeev and D. O. Pimanov},
     title = {Researching of {Periodic} {Solutions} in a {Mathematical} {Models} {of~Micromechanics} with {Pulsed} {Periodic} {Impact}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {122--140},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
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     url = {http://geodesic.mathdoc.fr/item/VNGU_2013_13_3_a11/}
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S. I. Fadeev; D. O. Pimanov. Researching of Periodic Solutions in a Mathematical Models of~Micromechanics with Pulsed Periodic Impact. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 3, pp. 122-140. http://geodesic.mathdoc.fr/item/VNGU_2013_13_3_a11/