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Bipenalty method from a frequency domain perspective
Author(s) -
Ilanko Sinniah,
Monterrubio Luis E.
Publication year - 2012
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.4266
Subject(s) - inertial frame of reference , stiffness , bounded function , frequency domain , penalty method , domain (mathematical analysis) , convergence (economics) , stability (learning theory) , natural frequency , eigenvalues and eigenvectors , mathematics , set (abstract data type) , control theory (sociology) , mathematical optimization , computer science , mathematical analysis , vibration , engineering , structural engineering , physics , classical mechanics , control (management) , quantum mechanics , machine learning , artificial intelligence , economics , programming language , economic growth
SUMMARY In a recent paper, it was shown that for time domain analysis, the simultaneous use of inertial and stiffness type penalty parameters to enforce constraints was found to yield accurate and converging results without causing any stability problems. From a frequency domain perspective, this is somewhat unexpected because the solution converges from below when stiffness penalty parameters are used to model constraints, and the convergence is from above when inertial penalty parameters are used. The purpose of this paper is to explain the effect of the simultaneous use of stiffness and inertial penalty parameters on the natural frequencies of constrained systems. In this work, it is shown that if suitably tuned, the bipenalty approach works well for frequency domain analysis also, and that with two different tuned set of stiffness and inertial penalty parameters, bounded solutions to the natural frequencies of constrained systems may be obtained. The method is applicable for any linear eigenvalue problem. Copyright © 2012 John Wiley & Sons, Ltd.