The Bernoulli-Euler and Timoshenko Theories in the Context of Research on the Characteristic Curves of Column with Different Boundary Conditions

摘要

In this paper the boundary problem taking into account the shearing effect and rotational inertia of cross-section (Timoshenko theory) has been presented. The column is loaded by external Euler's force with constant line of action. The results of numerical calculations of characteristic curves on the plane external load - vibration frequency obtained on the basis of Bernoulli-Euler and Timoshenko theories have been compared. Calculations have been performed for different slenderness parameter magnitude and types of support. It has been shown that the type of support has great influence on the difference in the obtained results on the basis of both considered theories.