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dc.contributor.authorMagrans Fontrodona, Francesc Xavier
dc.contributor.authorPoblet-Puig, Jordi
dc.contributor.authorRodríguez Ferran, Antonio
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental
dc.date.accessioned2016-08-29T10:40:45Z
dc.date.available2019-03-01T01:30:24Z
dc.date.issued2017-02
dc.identifier.citationMagrans, F.X., Poblet-Puig, J., Rodriguez-Ferran, A. The solution of linear mechanical systems in terms of path superposition. "Mechanical systems and signal processing", Febrer 2017, vol. 85, p. 111-125.
dc.identifier.issn0888-3270
dc.identifier.urihttp://hdl.handle.net/2117/89392
dc.description.abstractWe prove that the solution of any linear mechanical system can be expressed as a linear combination of signal transmission paths. This is done in the framework of the Global Transfer Direct Transfer (GTDT) formulation for vibroacoustic problems. Transmission paths are expressed as powers of the transfer matrix. The key idea of the proof is to generalise the Neumann series of the transfer matrix --which is convergent only if its spectral radius is smaller than one-- into a modified Neumann series that is convergent regardless of the eigenvalues of the transfer matrix. The modification consists in choosing the appropriate combination coefficients for the powers of the transfer matrix in the series. A recursive formula for the computation of these factors is derived. The theoretical results are illustrated by means of numerical examples. Finally, we show that the generalised Neumann series can be understood as an acceleration (i.e. convergence speedup) of the Jacobi iterative method.
dc.format.extent15 p.
dc.language.isoeng
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Física::Acústica::Física del so
dc.subject.lcshVibration--Measurement
dc.subject.lcshAcoustic models
dc.subject.otherTransfer matrix
dc.subject.otherPath
dc.subject.otherNeumann series
dc.subject.otherDirect transfer
dc.subject.otherGlobal transfer
dc.titleThe solution of linear mechanical systems in terms of path superposition
dc.typeArticle
dc.subject.lemacVibroacústica
dc.contributor.groupUniversitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria
dc.identifier.doi10.1016/j.ymssp.2016.07.044
dc.description.peerreviewedPeer Reviewed
dc.relation.publisherversionhttp://www.sciencedirect.com/science/article/pii/S0888327016302680
dc.rights.accessOpen Access
local.identifier.drac18817722
dc.description.versionPostprint (author's final draft)
local.citation.authorMagrans, F.X.; Poblet-Puig, J.; Rodriguez-Ferran, A.
local.citation.publicationNameMechanical systems and signal processing
local.citation.volume85
local.citation.startingPage111
local.citation.endingPage125


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