Explicit analysis of catasrophe on a Timoshenko beam (original) (raw)
Free related PDFsRelated papers
Free PDF
Recent literature has shown great interest for better understanding of the dynamics of slender structures. There are several classical beam models. Among them, the use of Timoshenko model, taking into account the shearability, is known to provide a very good estimation of thick beam dynamics especially for high frequencies. In this study a three dimensional shearable beam model is developped allowing finite rotations and strains. The present work follows the three dimensional finite beam theory introduced by Antman, Simo and others. Introducing a Cosserat director frame we develope a beam model entirely derived from the continuum mechanics theory. As an application of this theory we study free vibrations of a geometrically non-linear Timoshenko pre-stressed beam.
Free PDF
Free PDF
On Exact Analytical Solutions of the Timoshenko Beam Model Under Uniform and Variable Loads
2021
In this research work, we consider the mathematical model of the Timoshenko beam (TB) problem in the form of a boundary-value problem of a system of ordinary differential equations. Instead of numerical solution using finite difference and finite volume methods, an attempt is made to derive the exact analytical solutions of the model with boundary feedback for a better and explicit description of the rotation and displacement parameters of the TB structure model. The explicit analytical solutions have been successfully found for the uniform and real-time variable load cases. The rotation and displacement profiles obtained through the analytical solutions accurately picture the structure of the beam under uniform and variable loads.
Free PDF
Free PDF
Free PDF
Free PDF
Free PDF
Exact Static Analysis of In-Plane Curved Timoshenko Beams with Strong Nonlinear Boundary Conditions
Mathematical Problems in Engineering, 2015
Analytical solutions have been developed for nonlinear boundary problems. In this paper, the shifting function method is applied to develop the static deflection of in-plane curved Timoshenko beams with nonlinear boundary conditions. Three coupled governing differential equations are derived via the Hamilton’s principle. The mathematical modeling of the curved beam system can be decomposed into a complete sixth-order ordinary differential characteristic equation and the associated boundary conditions. It is shown that the proposed method is valid and performs well for problems with strong nonlinearity.
Free PDF
Free PDF
