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    Free Vibration of Combined Dynamical Systems

    Source: Journal of Engineering Mechanics:;1986:;Volume ( 112 ):;issue: 001
    Author:
    James W. Nicholson
    ,
    Lawrence A. Bergman
    DOI: 10.1061/(ASCE)0733-9399(1986)112:1(1)
    Publisher: American Society of Civil Engineers
    Abstract: A method for analyzing the free vibration of combined linear undamped dynamical systems attached at discrete points is shown. The method uses separation of variables to exhibit the harmonic motion of the system and to derive a generalized differential equation for the normal modes. Green's functions for the vibrating component systems are used to solve the generalized differential equation and derive the characteristic equation for the natural frequencies of the system. The characteristic equation can then be solved for the exact natural frequencies and exact normal modes. The method is demonstrated for two types of dynamical systems involving beams and oscillators. For two particular systems, approximate natural frequencies determined through a Galerkin's method and the finite element method are compared to the exact natural frequencies. The generalized orthogonality relation for each system is derived.
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      Free Vibration of Combined Dynamical Systems

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    contributor authorJames W. Nicholson
    contributor authorLawrence A. Bergman
    date accessioned2017-05-08T22:13:40Z
    date available2017-05-08T22:13:40Z
    date copyrightJanuary 1986
    date issued1986
    identifier other%28asce%290733-9399%281986%29112%3A1%281%29.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/74341
    description abstractA method for analyzing the free vibration of combined linear undamped dynamical systems attached at discrete points is shown. The method uses separation of variables to exhibit the harmonic motion of the system and to derive a generalized differential equation for the normal modes. Green's functions for the vibrating component systems are used to solve the generalized differential equation and derive the characteristic equation for the natural frequencies of the system. The characteristic equation can then be solved for the exact natural frequencies and exact normal modes. The method is demonstrated for two types of dynamical systems involving beams and oscillators. For two particular systems, approximate natural frequencies determined through a Galerkin's method and the finite element method are compared to the exact natural frequencies. The generalized orthogonality relation for each system is derived.
    publisherAmerican Society of Civil Engineers
    titleFree Vibration of Combined Dynamical Systems
    typeJournal Paper
    journal volume112
    journal issue1
    journal titleJournal of Engineering Mechanics
    identifier doi10.1061/(ASCE)0733-9399(1986)112:1(1)
    treeJournal of Engineering Mechanics:;1986:;Volume ( 112 ):;issue: 001
    contenttypeFulltext
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