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Cyclic steady states of nonlinear electro‐mechanical devices excited at resonance
Author(s) -
Brandstetter Gerd,
Govindjee Sanjay
Publication year - 2016
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5447
Subject(s) - nonlinear system , finite element method , resonance (particle physics) , steady state (chemistry) , control theory (sociology) , benchmark (surveying) , vibration , boundary value problem , mechanics , mechanical resonance , physics , computer science , mathematical analysis , mathematics , acoustics , chemistry , control (management) , geodesy , quantum mechanics , artificial intelligence , thermodynamics , geography , particle physics
Summary We present an efficient numerical method to solve for cyclic steady states of nonlinear electro‐mechanical devices excited at resonance. Many electro‐mechanical systems are designed to operate at resonance, where the ramp‐up simulation to steady state is computationally very expensive – especially when low damping is present. The proposed method relies on a Newton–Krylov shooting scheme for the direct calculation of the cyclic steady state, as opposed to a naïve transient time‐stepping from zero initial conditions. We use a recently developed high‐order Eulerian–Lagrangian finite element method in combination with an energy‐preserving dynamic contact algorithm in order to solve the coupled electro‐mechanical boundary value problem. The nonlinear coupled equations are evolved by means of an operator split of the mechanical and electrical problem with an explicit as well as implicit approach. The presented benchmark examples include the first three fundamental modes of a vibrating nanotube, as well as a micro‐electro‐mechanical disk resonator in dynamic steady contact. For the examples discussed, we observe power law computational speed‐ups of the form S = 0.6· ξ − 0.8 , where ξ is the linear damping ratio of the corresponding resonance frequency. Copyright © 2016 John Wiley & Sons, Ltd.