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DOI: 10.1007/s10884-007-9094-x Journal of Dynamics and Differential Equations, Vol. 20, No. 3, September 2008 ( 2007)
 

Summary: DOI: 10.1007/s10884-007-9094-x
Journal of Dynamics and Differential Equations, Vol. 20, No. 3, September 2008 ( 2007)
Dynamics of a Canonical Electrostatic MEMS/NEMS
System
Shangbing Ai1,3 and John A. Pelesko2
Received April 16, 2007
The mass-spring model of electrostatically actuated microelectromechanical sys-
tems (MEMS) or nanoelectromechanical systems (NEMS) is pervasive in the
MEMS and NEMS literature. Nonetheless a rigorous analysis of this model does
not exist. Here periodic solutions of the canonical mass-spring model in the vis-
cosity dominated time harmonic regime are studied. Ranges of the dimensionless
average applied voltage and dimensionless frequency of voltage variation are delin-
eated such that periodic solutions exist. Parameter ranges where such solutions fail
to exist are identified; this provides a dynamic analog to the static "pull-in" insta-
bility well known to MEMS/NEMS researchers.
KEY WORDS: MEMS; nanotechnology; electrostatics; periodic solutions;
saddle-node bifurcation; shooting method.
MATHEMATICS SUBJECT CLASSIFICATION (1991): 34C15; 34C60;
70K40.
1. INTRODUCTION

  

Source: Ai, Shangbing - Department of Mathematical Sciences, University of Alabama in Huntsville

 

Collections: Mathematics