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Inverse structural modification using constraints

Olsson, Pär LU and Lidström, Per LU (2007) In Journal of Sound and Vibration 303(3-5). p.767-779
Abstract
In a structural modification problem the mass and stiffness matrices are modified to obtain a desired spectrum. In this paper, this is done by imposing constraints on the structure. The undamped natural vibrations of a constrained linear structure are calculated by solving a generalized eigenvalue problem derived from the equations of motion for the constrained system involving Lagrangian multipliers. The coefficients of the constraint matrix are taken as design variables and a set of equations defining the inverse structural modification problem is formulated. This modification problem requires an iterative method for its solution. An algorithm based on Newton's method is employed. Each iteration step involves the calculation of a... (More)
In a structural modification problem the mass and stiffness matrices are modified to obtain a desired spectrum. In this paper, this is done by imposing constraints on the structure. The undamped natural vibrations of a constrained linear structure are calculated by solving a generalized eigenvalue problem derived from the equations of motion for the constrained system involving Lagrangian multipliers. The coefficients of the constraint matrix are taken as design variables and a set of equations defining the inverse structural modification problem is formulated. This modification problem requires an iterative method for its solution. An algorithm based on Newton's method is employed. Each iteration step involves the calculation of a rectangular Jacobian and the solving of an associated underdetermined system of linear equations. The system can be solved by using the Moore–Penrose inverse. The method is demonstrated in some numerical examples. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Sound and Vibration
volume
303
issue
3-5
pages
767 - 779
publisher
Elsevier
external identifiers
  • wos:000246661400022
  • scopus:34247186410
ISSN
0022-460X
DOI
10.1016/j.jsv.2007.02.003
language
English
LU publication?
yes
id
ba5b4ce0-63b7-4fcd-b55a-9ef0cd03b54a (old id 617722)
alternative location
http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6WM3-4NBXVJV-4-7&_cdi=6923&_user=745831&_orig=search&_coverDate=06%2F20%2F2007&_sk=996969996&view=c&wchp=dGLbVzz-zSkzS&md5=a41501c4a9af51664dfc38b7529b2aff&ie=/sdarticle.pdf
date added to LUP
2007-12-14 14:23:22
date last changed
2017-01-01 07:04:35
@article{ba5b4ce0-63b7-4fcd-b55a-9ef0cd03b54a,
  abstract     = {In a structural modification problem the mass and stiffness matrices are modified to obtain a desired spectrum. In this paper, this is done by imposing constraints on the structure. The undamped natural vibrations of a constrained linear structure are calculated by solving a generalized eigenvalue problem derived from the equations of motion for the constrained system involving Lagrangian multipliers. The coefficients of the constraint matrix are taken as design variables and a set of equations defining the inverse structural modification problem is formulated. This modification problem requires an iterative method for its solution. An algorithm based on Newton's method is employed. Each iteration step involves the calculation of a rectangular Jacobian and the solving of an associated underdetermined system of linear equations. The system can be solved by using the Moore–Penrose inverse. The method is demonstrated in some numerical examples.},
  author       = {Olsson, Pär and Lidström, Per},
  issn         = {0022-460X},
  language     = {eng},
  number       = {3-5},
  pages        = {767--779},
  publisher    = {Elsevier},
  series       = {Journal of Sound and Vibration},
  title        = {Inverse structural modification using constraints},
  url          = {http://dx.doi.org/10.1016/j.jsv.2007.02.003},
  volume       = {303},
  year         = {2007},
}