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1 Machine Dynamics Research

1 2014

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Free Vibrations and Stability of Geometrically Non-Linear Column Loaded by a Force Directed Towards a Positive Pole Partially Lying on Winkler Elastic Foundation

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Szmidla J. , Jurczyńska A.

tom Vol. 38, No. 2

59-68

The results of theoretical and numerical research on the stability and free vibrations of a geometricaly non-linear column loaded by a force directed towards a positive pole partially lying on Winkler elastic foundation are presented in the paper. Equations of motion and boundary conditions of considered structures were formulated on the basis of the principle of minimum potential energy and the Hamilton’s principle and then solved using the small parameter perturbation method. For non-linear system and linear column respectively, the value of bifurcation and critical load was obtained for various values of geometrical and physical parameters of considered structures. The ranges of local and global instability were determined. Application of Winkler’s elastic base causes an increase in the value of the bifurcation load and this is the method which allows the geometrically non-linear system to exit from the region of the local instability. The courses of natural vibration frequencies in relation to the external load and the influence of the physical and geometrical parameters on its value are determined.