The natural frequencies of toroidal shells of revolution with a hollow elliptical cross section and variable thickness are determined by the Ritz method from a three-dimensional theory, whereas traditional shell theories are mathematically two-dimensional. Instead of ordinary algebraic polynomials, the Legendre polynomials, which are mathematically orthonormal, are used as admissible functions. The present analysis is based upon the circular cylindrical coordinates, whereas toroidal coordinates have been used in general. The potential and kinetic energies of the torus are formulated, and upper bound values of the frequencies are obtained by minimizing the frequencies. Convergence to a four-digit exactitude is demonstrated for the first five frequencies of the torus. Comparisons are made between the frequencies from the present three-dimensional method, a two-dimensional thin-shell theory, and thin- and thick-ring theories. The present method is applicable to very thick shells as well as thin shells.


    Zugriff

    Zugriff prüfen

    Verfügbarkeit in meiner Bibliothek prüfen

    Bestellung bei Subito €


    Exportieren, teilen und zitieren



    Titel :

    Vibrations of a Torus with Hollow Elliptical Cross Section Having Variable Thickness


    Beteiligte:
    Kang, Jae-Hoon (Autor:in)

    Erschienen in:

    AIAA Journal ; 56 , 1 ; 376-386


    Erscheinungsdatum :

    2017-09-11


    Format / Umfang :

    11 pages




    Medientyp :

    Aufsatz (Zeitschrift)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch





    Torsional vibrations and design charts for hollow shafts with variable cross section

    Rezeka,S.F. / Alexandria Univ.,Faculty of Engineering,EG | Kraftfahrwesen | 1989



    AIR DATA PROBE WITH ELLIPTICAL CROSS SECTION

    BRUSIUS NATHAN | Europäisches Patentamt | 2017

    Freier Zugriff