A perturbation method for evaluating nonlinear normal modes of a piecewise linear two-degrees-of-freedom system
type: Item
instance of: scholarly article
title: A perturbation method for evaluating nonlinear normal modes of a piecewise linear two-degrees-of-freedom system
zbMATH Open document ID: 1191.70010
published in: Nonlinear Dynamics
publication date: 2009-09-11T00:00:00Z
review text: The aim of this paper is to investigate the dynamics of systems expected to exhibit superabundant modes. An important example of piecewise smooth system is considered, as a beam with a breathing crack by taking advantage of related works presnt in literature. The Lindstedt-Poincaré method is applied under the hypothesis the discontinuity is small. Passive and active frequencies, modified by the same damage-dependent factor, contribute to the motion although they are incommensurable. Results of the stability analysis show that while the second mode is always stable, the first mode is unstable for some values of the damage parameter. Numerical results, obtained by a Poincaré map approach, confirm the perturbation results and also show the existence of superabundant normal modes which arise in the unstable interval of the first mode.
reviewed by: Vasile Marinca
Mathematics Subject Classification ID: 70K45
Mathematics Subject Classification ID: 70K60
Mathematics Subject Classification ID: 70K20
zbMATH DE Number: 5603311
zbMATH Keywords: nonlinear normal modes
zbMATH Keywords: piecewise-linear systems
zbMATH Keywords: perturbation methods
zbMATH Keywords: damaged systems
zbMATH Keywords: cracked beams
author: Fabrizio Vestroni
author: A. Luongo
author: Achille Paolone
MaRDI profile type: Publication
full work available at URL: s11071-008-9337-3
OpenAlex ID: W2164772164
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DOI: 10.1007/S11071-008-9337-3
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description: scientific article; zbMATH DE number 5603311