Linearized equations of motion in multibody dynamics
(2014) In Mathematics and Mechanics of Solids 21(4). p.454505 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.
(Less)
 author
 Lidström, P. ^{LU}
 organization
 publishing date
 2014
 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
 10812865
 DOI
 10.1177/1081286514526215
 language
 English
 LU publication?
 yes
 id
 766471bee31a4d778771a29302c9761a
 date added to LUP
 20160926 11:06:11
 date last changed
 20160926 11:06:11
@misc{766471bee31a4d778771a29302c9761a, 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 = {10812865}, keyword = {generalized eigenvalue problem,linearized equations,Multibody dynamics,multiple roots,vibrations}, language = {eng}, number = {4}, pages = {454505}, publisher = {ARRAY(0x937e6d8)}, 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}, }