Elishakoff et al. once proposed a novel physics-based, low-frequency correction to the Timoshenko–Ehrenfest beam theory. The corrected beam theory is simpler than the classical one because it leads to a single frequency series in the vibrating analysis, without loss of the effect of shear deformation and rotary inertia. In this paper, a further modification is proposed based on Elishakoff’s correction such that the resulting single frequency series fits quite well with the first branch of the Timoshenko–Ehrenfest beam theory up to a relatively high frequency (i.e., the cutoff frequency of Timoshenko–Ehrenfest beams). Most strikingly, the present modification is found to be suitable not only for homogeneous and uniform beams but also for a wide class of beam structures with axial inhomogeneity and/or variable cross section. An inhomogeneous and nonuniform beam with two sharp ends is analytically studied in detail using several different engineering beam models, which fully verifies the necessity and high accuracy of the present modification, particularly for beam structures composed of materials with negative Poisson’s ratio.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Novel Modification to the Timoshenko–Ehrenfest Theory for Inhomogeneous and Nonuniform Beams


    Contributors:

    Published in:

    AIAA Journal ; 58 , 2 ; 939-948


    Publication date :

    2020-02-01




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English




    Nonuniform Isospectrals of Uniform Timoshenko Beams

    Bhat K, Srivatsa / Ranjan, Ganguli | AIAA | 2019


    Energy Transformation to Generalized Timoshenko Form for Nonuniform Beams

    Ho, Jimmy C. / Hodges, Dewey H. / Yu, Wenbin | AIAA | 2010




    Slope-Inertia Model of Non-Uniform and Inhomogeneous Bresse-Timoshenko Beams

    Bhat K, Srivatsa / Sarkar, Korak / Ganguli, Ranjan et al. | AIAA | 2018