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    An Exact Fourier Series Method for the Vibration Analysis of Multispan Beam Systems

    Source: Journal of Computational and Nonlinear Dynamics:;2009:;volume( 004 ):;issue: 002::page 21001
    Author:
    Wen L. Li
    ,
    Hongan Xu
    DOI: 10.1115/1.3079681
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: An exact Fourier series method is developed for the vibration analysis of multispan beam systems. In this method, the displacement on each beam is expressed as a Fourier series expansion plus an auxiliary closed-form function such as polynomials. The auxiliary function is used to deal with all the possible discontinuities, at the end points, with the original displacement function and its derivatives when they are periodically extended over the entire x-axis as implied by a Fourier series representation. As a result, not only is it always possible to expand the beam displacements into Fourier series under any boundary conditions, but also the series solution will be substantially improved in terms of its accuracy and convergence. Mathematically, the current Fourier series expansion represents an exact solution to a class of beam problems in the sense that both the governing equations and the boundary/coupling conditions are simultaneously satisfied to any specified degree of accuracy. In the multispan beam system model, any two adjacent beams are generally connected together via a pair of linear and rotational springs, allowing a better modeling of many real-world joints. Each beam in the system can also be independently and elastically restrained at its ends so that all boundary conditions including the classical homogeneous boundary conditions at the end and intermediate supports can be universally dealt with by simply varying the stiffnesses of the restraining springs accordingly, which does not involve any modification of basis functions, formulations, or solution procedures. The excellent accuracy and convergence of this series solution is demonstrated through numerical examples.
    keyword(s): Vibration , Boundary-value problems , Displacement , Fourier series , Functions , Springs , Vibration analysis , Equations , Stiffness , Polynomials , Shapes , Frequency AND Junctions ,
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      An Exact Fourier Series Method for the Vibration Analysis of Multispan Beam Systems

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    http://yetl.yabesh.ir/yetl1/handle/yetl/140077
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    contributor authorWen L. Li
    contributor authorHongan Xu
    date accessioned2017-05-09T00:31:54Z
    date available2017-05-09T00:31:54Z
    date copyrightApril, 2009
    date issued2009
    identifier issn1555-1415
    identifier otherJCNDDM-25676#021001_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/140077
    description abstractAn exact Fourier series method is developed for the vibration analysis of multispan beam systems. In this method, the displacement on each beam is expressed as a Fourier series expansion plus an auxiliary closed-form function such as polynomials. The auxiliary function is used to deal with all the possible discontinuities, at the end points, with the original displacement function and its derivatives when they are periodically extended over the entire x-axis as implied by a Fourier series representation. As a result, not only is it always possible to expand the beam displacements into Fourier series under any boundary conditions, but also the series solution will be substantially improved in terms of its accuracy and convergence. Mathematically, the current Fourier series expansion represents an exact solution to a class of beam problems in the sense that both the governing equations and the boundary/coupling conditions are simultaneously satisfied to any specified degree of accuracy. In the multispan beam system model, any two adjacent beams are generally connected together via a pair of linear and rotational springs, allowing a better modeling of many real-world joints. Each beam in the system can also be independently and elastically restrained at its ends so that all boundary conditions including the classical homogeneous boundary conditions at the end and intermediate supports can be universally dealt with by simply varying the stiffnesses of the restraining springs accordingly, which does not involve any modification of basis functions, formulations, or solution procedures. The excellent accuracy and convergence of this series solution is demonstrated through numerical examples.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleAn Exact Fourier Series Method for the Vibration Analysis of Multispan Beam Systems
    typeJournal Paper
    journal volume4
    journal issue2
    journal titleJournal of Computational and Nonlinear Dynamics
    identifier doi10.1115/1.3079681
    journal fristpage21001
    identifier eissn1555-1423
    keywordsVibration
    keywordsBoundary-value problems
    keywordsDisplacement
    keywordsFourier series
    keywordsFunctions
    keywordsSprings
    keywordsVibration analysis
    keywordsEquations
    keywordsStiffness
    keywordsPolynomials
    keywordsShapes
    keywordsFrequency AND Junctions
    treeJournal of Computational and Nonlinear Dynamics:;2009:;volume( 004 ):;issue: 002
    contenttypeFulltext
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