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    The second strain gradient theory-based Timoshenko beam model

    , Article JVC/Journal of Vibration and Control ; Volume 23, Issue 13 , 2017 , Pages 2155-2166 ; 10775463 (ISSN) Asghari, M ; Momeni, S. A ; Vatankhah, R ; Sharif University of Technology
    SAGE Publications Inc  2017
    The governing equations of motion, together with the associated boundary conditions, are derived for the second strain gradient Timoshenko micro- and nano-beams. The second strain gradient theory is a highly powerful nonclassical continuum theory, capable of capturing the size effects in micro- and nano-scale structures. In case studies, the static and free-vibration behaviors of a hinged-hinged beam are investigated utilizing the presented second strain gradient theory-based Timoshenko beam model. The obtained results are compared with those of the available models in the literature, which are based on the (first) strain gradient theory, the modified couple stress theory, and the classical...