Original scientific paper
Timoshenko Beam Theory 93 Years Later – over Bridges to Nanotubes and Ultra Large Ships
Ivo Senjanović
; Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, Croatia
Nikola Vladimir
; Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb
Marko Tomić
; Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb
Neven Hadžić
; Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb
Abstract
An outline of the Timoshenko beam theory, which deals with deflection and cross-section rotation as the basic variables, is presented. It is modified by decomposing 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. The solution is given for natural vibrations. Nonlocal stress parameter is taken into account for vibration analysis of nanotube embedded in an elastic medium. The 4th order partial differential equation for flexural vibration is extended to the 6th order one. Nanotube response to moving nanoparticle gravity load is analyzed by employing modal superposition method, separation of variables, Galerkin method and harmonic balance method. In addition coupled flexural and torsional vibrations of a thin-walled girder are considered. The modified Timoshenko beam theory is applied for flexural vibrations while the complex torsional beam theory with warping cross-section is worked out in an analogical way. For vibration analysis of nonprismatic ship hull an advanced beam finite element is created. Application of the developed theory is illustrated in the case of nanotube and ultra large container ship vibrations.
Keywords
Timoshenko beam theory; nanotube; moving load; thin-walled girder; flexural vibrations; torsional vibrations; container ship
Hrčak ID:
141344
URI
Publication date:
14.7.2015.
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