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Structural Engineering and Mechanics Volume 48, Number 4, November25 2013 , pages 519-545 DOI: https://doi.org/10.12989/sem.2013.48.4.519 |
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Physical insight into Timoshenko beam theory and its modification with extension |
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Ivo Senjanović and Nikola Vladimir
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| Abstract | ||
| An outline of the Timoshenko beam theory is presented. Two differential equations of motion in terms of deflection and rotation are comprised into single equation with deflection and analytical solutions of natural vibrations for different boundary conditions are given. Double frequency phenomenon for simply supported beam is investigated. The Timoshenko beam theory is modified by decomposition of total deflection into pure bending deflection and shear deflection, and total rotation into bending rotation and axial shear angle. The governing equations are condensed into two independent equations of motion, one for flexural and another for axial shear vibrations. Flexural vibrations of a simply supported, clamped and free beam are analysed by both theories and the same natural frequencies are obtained. That fact is proved in an analytical way. Axial shear vibrations are analogous to stretching vibrations on an axial elastic support, resulting in an additional response spectrum, as a novelty. Relationship between parameters in beam response functions of all type of vibrations is analysed. | ||
| Key Words | ||
| Timoshenko beam theory; flexural vibration; axial shear vibration; vibration parameter; analytical solution; double frequency phenomenon | ||
| Address | ||
| Ivo Senjanović and Nikola Vladimir : Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10000 Zagreb, Croatia | ||