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Summary: JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 13, NO. 5, OCTOBER 2004 737
Full-Lagrangian Schemes for Dynamic Analysis of
Electrostatic MEMS
Sudipto K. De and N. R. Aluru, Member, IEEE, Associate Member, ASME
Abstract--Dynamic analysis of microelectromechanical systems
(MEMS) is characterized by the nonlinear coupling of electrical
and mechanical domains. The nonlinear coupling between the
two domains gives rise to several interesting dynamic phenomena
besides the well established pull-in phenomenon in electrostatic
MEMS. For proper understanding and detailed exploration of
MEMS dynamics, it is important to have a reliable and effi-
cient physical level simulation method. In this paper, we develop
relaxation and Newton schemes based on a Lagrangian descrip-
tion of both the mechanical and the electrical domains for the
analysis of MEMS dynamics. The application of a Lagrangian
description for both mechanical and electrostatic analysis makes
this method far more efficient than standard semi-Lagrangian
scheme-based analysis of MEMS dynamics. A major advantage
of the full-Lagrangian scheme is in the accurate computation of
the interdomain coupling term (mechanical to electrical) in the
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