Recursive Solution Procedures for Flexible Multibody Systems: Comparing Condensation and Transfer Matrix Methods

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    Abstract

    In this work two different recursive solution procedures for flexible multibody systems are considered: the condensation method and the transfer matrix method. A comparison between these methods is made based on the equation of motion of an arbitrary 3D linear elastic body, in which the absolute interface coordinates are used as generalized coordinates. To this end, the equation of motion in a floating frame of reference formulation is rewritten in terms absolute interface coordinates for a body that has two interface points. In terms of these absolute coordinates, the condensation method can be given a clear physical interpretation related to added effective mass. This method is compared with a recursive solution procedure based on transfer matrices. This transfer matrix method may have advantages in the case of closed-loop systems and systems that consist of a chain of identical bodies.
    Original languageEnglish
    Title of host publicationECCOMAS Thematic Conference on Multibody Dynamics
    Subtitle of host publicationPrague, June 19-22, 2017 : conference proceedings
    EditorsMichael Valasek, Zbynek Sika, Tomas Vampola
    PublisherCzech Technical University
    Pages57-61
    Number of pages5
    ISBN (Electronic)978-80-01-6174-9
    ISBN (Print)978-80-01-06173-2
    Publication statusPublished - 19 Jun 2017
    EventMultibody Dynamics 2017: 8th ECCOMAS Thematic Conference - Czech Technical University, Prague, Czech Republic
    Duration: 19 Jun 201722 Jun 2017
    Conference number: 8
    http://multibody2017.cz/

    Conference

    ConferenceMultibody Dynamics 2017
    CountryCzech Republic
    CityPrague
    Period19/06/1722/06/17
    Internet address

    Fingerprint

    Transfer matrix method
    Equations of motion
    Condensation
    Closed loop systems

    Keywords

    • Flexible multibody dynamics
    • Recursive formulations
    • Floating frame of reference
    • Transfer matrix method

    Cite this

    Schilder, J., Ellenbroek, M., & de Boer, A. (2017). Recursive Solution Procedures for Flexible Multibody Systems: Comparing Condensation and Transfer Matrix Methods. In M. Valasek, Z. Sika, & T. Vampola (Eds.), ECCOMAS Thematic Conference on Multibody Dynamics: Prague, June 19-22, 2017 : conference proceedings (pp. 57-61). Czech Technical University.
    Schilder, Jurnan ; Ellenbroek, Marcel ; de Boer, André. / Recursive Solution Procedures for Flexible Multibody Systems : Comparing Condensation and Transfer Matrix Methods. ECCOMAS Thematic Conference on Multibody Dynamics: Prague, June 19-22, 2017 : conference proceedings. editor / Michael Valasek ; Zbynek Sika ; Tomas Vampola. Czech Technical University, 2017. pp. 57-61
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    title = "Recursive Solution Procedures for Flexible Multibody Systems: Comparing Condensation and Transfer Matrix Methods",
    abstract = "In this work two different recursive solution procedures for flexible multibody systems are considered: the condensation method and the transfer matrix method. A comparison between these methods is made based on the equation of motion of an arbitrary 3D linear elastic body, in which the absolute interface coordinates are used as generalized coordinates. To this end, the equation of motion in a floating frame of reference formulation is rewritten in terms absolute interface coordinates for a body that has two interface points. In terms of these absolute coordinates, the condensation method can be given a clear physical interpretation related to added effective mass. This method is compared with a recursive solution procedure based on transfer matrices. This transfer matrix method may have advantages in the case of closed-loop systems and systems that consist of a chain of identical bodies.",
    keywords = "Flexible multibody dynamics, Recursive formulations, Floating frame of reference, Transfer matrix method",
    author = "Jurnan Schilder and Marcel Ellenbroek and {de Boer}, Andr{\'e}",
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    Schilder, J, Ellenbroek, M & de Boer, A 2017, Recursive Solution Procedures for Flexible Multibody Systems: Comparing Condensation and Transfer Matrix Methods. in M Valasek, Z Sika & T Vampola (eds), ECCOMAS Thematic Conference on Multibody Dynamics: Prague, June 19-22, 2017 : conference proceedings. Czech Technical University, pp. 57-61, Multibody Dynamics 2017, Prague, Czech Republic, 19/06/17.

    Recursive Solution Procedures for Flexible Multibody Systems : Comparing Condensation and Transfer Matrix Methods. / Schilder, Jurnan; Ellenbroek, Marcel; de Boer, André.

    ECCOMAS Thematic Conference on Multibody Dynamics: Prague, June 19-22, 2017 : conference proceedings. ed. / Michael Valasek; Zbynek Sika; Tomas Vampola. Czech Technical University, 2017. p. 57-61.

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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    N2 - In this work two different recursive solution procedures for flexible multibody systems are considered: the condensation method and the transfer matrix method. A comparison between these methods is made based on the equation of motion of an arbitrary 3D linear elastic body, in which the absolute interface coordinates are used as generalized coordinates. To this end, the equation of motion in a floating frame of reference formulation is rewritten in terms absolute interface coordinates for a body that has two interface points. In terms of these absolute coordinates, the condensation method can be given a clear physical interpretation related to added effective mass. This method is compared with a recursive solution procedure based on transfer matrices. This transfer matrix method may have advantages in the case of closed-loop systems and systems that consist of a chain of identical bodies.

    AB - In this work two different recursive solution procedures for flexible multibody systems are considered: the condensation method and the transfer matrix method. A comparison between these methods is made based on the equation of motion of an arbitrary 3D linear elastic body, in which the absolute interface coordinates are used as generalized coordinates. To this end, the equation of motion in a floating frame of reference formulation is rewritten in terms absolute interface coordinates for a body that has two interface points. In terms of these absolute coordinates, the condensation method can be given a clear physical interpretation related to added effective mass. This method is compared with a recursive solution procedure based on transfer matrices. This transfer matrix method may have advantages in the case of closed-loop systems and systems that consist of a chain of identical bodies.

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    KW - Recursive formulations

    KW - Floating frame of reference

    KW - Transfer matrix method

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    EP - 61

    BT - ECCOMAS Thematic Conference on Multibody Dynamics

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    A2 - Sika, Zbynek

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    Schilder J, Ellenbroek M, de Boer A. Recursive Solution Procedures for Flexible Multibody Systems: Comparing Condensation and Transfer Matrix Methods. In Valasek M, Sika Z, Vampola T, editors, ECCOMAS Thematic Conference on Multibody Dynamics: Prague, June 19-22, 2017 : conference proceedings. Czech Technical University. 2017. p. 57-61