Eigensolutions of nonviscously damped systems based on the fixed-point iteration

In this paper, nonviscous, nonproportional, symmetric vibrating structures are considered. Nonviscously damped systems present dissipative forces depending on the time history of the response via kernel hereditary functions. Solutions of the free motion equation leads to a nonlinear eigenvalue probl...

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Veröffentlicht in:Journal of sound and vibration Jg. 418; S. 100 - 121
1. Verfasser: Lázaro, Mario
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier Ltd 31.03.2018
Elsevier Science Ltd
Schlagworte:
Convergence
Damping
Decay rate
Degrees of freedom
Eigenvalues
Eigenvalues and eigenvectors
Eigenvectors
Fixed-point iteration
Iterative methods
Mathematical models
Nonproportional damping
Nonviscous damping
Recursive algorithms
Recursive functions
Recursive methods
Sequences
Stiffness
Vibration
Vibration analysis
Viscoelasticity
Viscous damping
Fixed-point iteration
Nonproportional damping
Recursive functions
Eigenvalues and eigenvectors
Nonviscous damping
Viscous damping
ISSN:0022-460X, 1095-8568
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Zusammenfassung:In this paper, nonviscous, nonproportional, symmetric vibrating structures are considered. Nonviscously damped systems present dissipative forces depending on the time history of the response via kernel hereditary functions. Solutions of the free motion equation leads to a nonlinear eigenvalue problem involving mass, stiffness and damping matrices, this latter as dependent on frequency. Viscous damping can be considered as a particular case, involving damping forces as function of the instantaneous velocity of the degrees of freedom. In this work, a new numerical procedure to compute eigensolutions is proposed. The method is based on the construction of certain recursive functions which, under a iterative scheme, allow to reach eigenvalues and eigenvectors simultaneously and avoiding computation of eigensensitivities. Eigenvalues can be read then as fixed–points of those functions. A deep analysis of the convergence is carried out, focusing specially on relating the convergence conditions and error–decay rate to the damping model features, such as the nonproportionality and the viscoelasticity. The method is validated using two 6 degrees of freedom numerical examples involving both nonviscous and viscous damping and a continuous system with a local nonviscous damper. The convergence and the sequences behavior are in agreement with the results foreseen by the theory.
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ISSN:0022-460X
1095-8568
DOI:10.1016/j.jsv.2017.12.025