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    Rayleigh Quotient and Dissipative Systems

    Source: Journal of Applied Mechanics:;2008:;volume( 075 ):;issue: 006::page 61005
    Author:
    A. Srikantha Phani
    ,
    S. Adhikari
    DOI: 10.1115/1.2910898
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: Rayleigh quotients in the context of linear, nonconservative vibrating systems with viscous and nonviscous dissipative forces are studied in this paper. Of particular interest is the stationarity property of Rayleigh-like quotients for dissipative systems. Stationarity properties are examined based on the perturbation theory. It is shown that Rayleigh quotients with stationary properties exist for systems with proportional viscous and nonviscous damping forces. It is also shown that the stationarity property of Rayleigh quotients in the case of nonproportional damping (viscous and nonviscous) is conditional upon the diagonal dominance of the modal damping matrix.
    keyword(s): Damping , Equations AND Eigenvalues ,
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      Rayleigh Quotient and Dissipative Systems

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    contributor authorA. Srikantha Phani
    contributor authorS. Adhikari
    date accessioned2017-05-09T00:26:31Z
    date available2017-05-09T00:26:31Z
    date copyrightNovember, 2008
    date issued2008
    identifier issn0021-8936
    identifier otherJAMCAV-26727#061005_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/137200
    description abstractRayleigh quotients in the context of linear, nonconservative vibrating systems with viscous and nonviscous dissipative forces are studied in this paper. Of particular interest is the stationarity property of Rayleigh-like quotients for dissipative systems. Stationarity properties are examined based on the perturbation theory. It is shown that Rayleigh quotients with stationary properties exist for systems with proportional viscous and nonviscous damping forces. It is also shown that the stationarity property of Rayleigh quotients in the case of nonproportional damping (viscous and nonviscous) is conditional upon the diagonal dominance of the modal damping matrix.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleRayleigh Quotient and Dissipative Systems
    typeJournal Paper
    journal volume75
    journal issue6
    journal titleJournal of Applied Mechanics
    identifier doi10.1115/1.2910898
    journal fristpage61005
    identifier eissn1528-9036
    keywordsDamping
    keywordsEquations AND Eigenvalues
    treeJournal of Applied Mechanics:;2008:;volume( 075 ):;issue: 006
    contenttypeFulltext
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