This paper discusses the development of numerical methods for calculating the natural frequencies of tapered beams that are laterally restrained by elastic springs. In formulating the governing equation of the beam, each elastic spring is modeled as a discrete Winkler foundation of the finite longitudinal length, and the effect of axial load is included. By using this model, the differential equation governing the free vibration of the beam is derived, which is solved numerically. The Runge-Kutta method is used to integrate the differential equation, and the determinant search method combined with the Regula-Falsi method is used to determine the eingenvalues, namely, the natural frequencies. In the numerical examples, clamped-clamped, clamped-hinged, hinged-clamped and hinged-hinged end constraints are considered. The numerical results, including the frequency parameters and mode shapes of free vibrations are presented in non-dimensional forms.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Free vibrations of tapered beams laterally restrained by elastic springs


    Additional title:

    KSCE J Civ Eng


    Contributors:

    Published in:

    Publication date :

    2003-03-01


    Size :

    7 pages




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English




    Buckling loads of linearly tapered columns laterally restrained by multiple elastic springs

    Lee, Byoung Koo / Li, Guangfan / Kim, Suk Ki et al. | Springer Verlag | 2003


    Large amplitude free vibrations of tapered beams

    RAJU, L. S. / RAJU, K. K. / NASA, Langley Research Center et al. | AIAA | 1976


    Free vibrations of tapered beams with general boundary condition

    Lee, Byoung Koo / Lee, Jong Kook / Lee, Tae Eun et al. | Springer Verlag | 2002