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    Almost Classically Damped Continuous Linear Systems

    Source: Journal of Applied Mechanics:;1998:;volume( 065 ):;issue: 004::page 1022
    Author:
    S. Natsiavas
    ,
    J. L. Beck
    DOI: 10.1115/1.2791896
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: The dynamic response of a general class of continuous linear vibrating systems is analyzed which possess damping properties close to those resulting in classical (uncoupled) normal modes. First, conditions are given for the existence of classical modes of vibration in a continuous linear system, with special attention being paid to the boundary conditions. Regular perturbation expansions in terms of undamped modeshapes are then utilized for analyzing the eigenproblem as well as the vibration response of almost classically damped systems. The analysis is based on a proper splitting of the damping operators in both the field equations and the boundary conditions. The main advantage of this approach is that it allows application of standard modal analysis methodologies so that the problem is reduced to that of finding the frequencies and mode shapes of the corresponding undamped system. The approach is illustrated by two simple examples involving rod and beam vibrations.
    keyword(s): Linear systems , Vibration , Boundary-value problems , Damping , Shapes , Dynamic response , Equations AND Frequency ,
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      Almost Classically Damped Continuous Linear Systems

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    http://yetl.yabesh.ir/yetl1/handle/yetl/119864
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    contributor authorS. Natsiavas
    contributor authorJ. L. Beck
    date accessioned2017-05-08T23:55:35Z
    date available2017-05-08T23:55:35Z
    date copyrightDecember, 1998
    date issued1998
    identifier issn0021-8936
    identifier otherJAMCAV-26457#1022_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/119864
    description abstractThe dynamic response of a general class of continuous linear vibrating systems is analyzed which possess damping properties close to those resulting in classical (uncoupled) normal modes. First, conditions are given for the existence of classical modes of vibration in a continuous linear system, with special attention being paid to the boundary conditions. Regular perturbation expansions in terms of undamped modeshapes are then utilized for analyzing the eigenproblem as well as the vibration response of almost classically damped systems. The analysis is based on a proper splitting of the damping operators in both the field equations and the boundary conditions. The main advantage of this approach is that it allows application of standard modal analysis methodologies so that the problem is reduced to that of finding the frequencies and mode shapes of the corresponding undamped system. The approach is illustrated by two simple examples involving rod and beam vibrations.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleAlmost Classically Damped Continuous Linear Systems
    typeJournal Paper
    journal volume65
    journal issue4
    journal titleJournal of Applied Mechanics
    identifier doi10.1115/1.2791896
    journal fristpage1022
    journal lastpage1031
    identifier eissn1528-9036
    keywordsLinear systems
    keywordsVibration
    keywordsBoundary-value problems
    keywordsDamping
    keywordsShapes
    keywordsDynamic response
    keywordsEquations AND Frequency
    treeJournal of Applied Mechanics:;1998:;volume( 065 ):;issue: 004
    contenttypeFulltext
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