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Linearized equations of motion in multibody dynamics

Lidström, P. LU (2014) In Mathematics and Mechanics of Solids 21(4). p.454-505
Abstract

In this paper the linearized equations of motion in multibody dynamics are derived. Explicit expressions for the coefficient matrices are presented and given their physical interpretations. The equations of motion are presented in terms of the mechanical stiffness, its adjoint and the associated differential operators. It is demonstrated how the adjoint matrix may be used to find solutions to the associated algebraic eigenvalue problem. The case of multiple roots of the characteristic equation will result in a generalized eigenvalue problem involving the notion of a Jordan chain. Qualitative properties of the spectrum are derived without explicitly solving the characteristic equation. Finally, the mechanical admittance and its spectral... (More)

In this paper the linearized equations of motion in multibody dynamics are derived. Explicit expressions for the coefficient matrices are presented and given their physical interpretations. The equations of motion are presented in terms of the mechanical stiffness, its adjoint and the associated differential operators. It is demonstrated how the adjoint matrix may be used to find solutions to the associated algebraic eigenvalue problem. The case of multiple roots of the characteristic equation will result in a generalized eigenvalue problem involving the notion of a Jordan chain. Qualitative properties of the spectrum are derived without explicitly solving the characteristic equation. Finally, the mechanical admittance and its spectral representations are discussed.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
generalized eigenvalue problem, linearized equations, Multibody dynamics, multiple roots, vibrations
in
Mathematics and Mechanics of Solids
volume
21
issue
4
pages
52 pages
publisher
SAGE Publications
external identifiers
  • Scopus:84962359828
ISSN
1081-2865
DOI
10.1177/1081286514526215
language
English
LU publication?
yes
id
766471be-e31a-4d77-8771-a29302c9761a
date added to LUP
2016-09-26 11:06:11
date last changed
2017-01-01 08:35:12
@article{766471be-e31a-4d77-8771-a29302c9761a,
  abstract     = {<p>In this paper the linearized equations of motion in multibody dynamics are derived. Explicit expressions for the coefficient matrices are presented and given their physical interpretations. The equations of motion are presented in terms of the mechanical stiffness, its adjoint and the associated differential operators. It is demonstrated how the adjoint matrix may be used to find solutions to the associated algebraic eigenvalue problem. The case of multiple roots of the characteristic equation will result in a generalized eigenvalue problem involving the notion of a Jordan chain. Qualitative properties of the spectrum are derived without explicitly solving the characteristic equation. Finally, the mechanical admittance and its spectral representations are discussed.</p>},
  author       = {Lidström, P.},
  issn         = {1081-2865},
  keyword      = {generalized eigenvalue problem,linearized equations,Multibody dynamics,multiple roots,vibrations},
  language     = {eng},
  number       = {4},
  pages        = {454--505},
  publisher    = {SAGE Publications},
  series       = {Mathematics and Mechanics of Solids},
  title        = {Linearized equations of motion in multibody dynamics},
  url          = {http://dx.doi.org/10.1177/1081286514526215},
  volume       = {21},
  year         = {2014},
}