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On the natural vibrations of linear structures with constraints

Lidström, Per LU and Olsson, Pär LU (2007) In Journal of Sound and Vibration 301(1-2). p.341-354
Abstract
The undamped natural vibrations of a constrained linear structure are given by the solutions to a generalized eigenvalue problem derived from the equations of motion for the constrained system involving Lagrangian multipliers. The eigenvalue problem derived is defined by the mass matrix of the unconstrained structure and a non-symmetric and singular stiffness matrix for the constrained system. The character of the solution of the eigenvalue problem of the constrained system is stated and proved in a Theorem. Applications of the constrained eigenvalue problem to some simple structures are demonstrated. Finally a condition for the calculation of the damped natural vibrations for the constrained structure in terms of the undamped mode shapes... (More)
The undamped natural vibrations of a constrained linear structure are given by the solutions to a generalized eigenvalue problem derived from the equations of motion for the constrained system involving Lagrangian multipliers. The eigenvalue problem derived is defined by the mass matrix of the unconstrained structure and a non-symmetric and singular stiffness matrix for the constrained system. The character of the solution of the eigenvalue problem of the constrained system is stated and proved in a Theorem. Applications of the constrained eigenvalue problem to some simple structures are demonstrated. Finally a condition for the calculation of the damped natural vibrations for the constrained structure in terms of the undamped mode shapes is formulated. (c) 2006 Elsevier Ltd. All rights reserved. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Sound and Vibration
volume
301
issue
1-2
pages
341 - 354
publisher
Elsevier
external identifiers
  • wos:000244183500020
  • scopus:33846257665
ISSN
0022-460X
DOI
10.1016/j.jsv.2006.10.003
language
English
LU publication?
yes
id
c7728097-e357-4965-8bc6-bcfabeb20b20 (old id 674554)
date added to LUP
2007-12-14 14:42:02
date last changed
2017-01-01 06:49:25
@article{c7728097-e357-4965-8bc6-bcfabeb20b20,
  abstract     = {The undamped natural vibrations of a constrained linear structure are given by the solutions to a generalized eigenvalue problem derived from the equations of motion for the constrained system involving Lagrangian multipliers. The eigenvalue problem derived is defined by the mass matrix of the unconstrained structure and a non-symmetric and singular stiffness matrix for the constrained system. The character of the solution of the eigenvalue problem of the constrained system is stated and proved in a Theorem. Applications of the constrained eigenvalue problem to some simple structures are demonstrated. Finally a condition for the calculation of the damped natural vibrations for the constrained structure in terms of the undamped mode shapes is formulated. (c) 2006 Elsevier Ltd. All rights reserved.},
  author       = {Lidström, Per and Olsson, Pär},
  issn         = {0022-460X},
  language     = {eng},
  number       = {1-2},
  pages        = {341--354},
  publisher    = {Elsevier},
  series       = {Journal of Sound and Vibration},
  title        = {On the natural vibrations of linear structures with constraints},
  url          = {http://dx.doi.org/10.1016/j.jsv.2006.10.003},
  volume       = {301},
  year         = {2007},
}