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The Tapered Column Shape Optimisation in a Plane Perpendicular to the Buckling Plane Subjected to a Load by the Follower Force Directed to the Positive Pole

Szmidla J., Jurczyńska A.

Machine Dynamics Research

2015

Vol. 39, No. 2

33-44

The results of theoretical and numerical research on shape optimisation of cantilever column subjected to a load by the follower force directed towards the positive pole are presented in this paper. Deflection line and cross section area equations of considered column and appropriate boundary problem were derived on the basis of static criterion of stability assuming constant volume of the rod. Having regard to the column’s taper in the plane perpendicular to the buckling plane, an extra conditions due to allowable stresses of structure were taken into account. Optimal shape and the critical load value of system meeting the compressive stressrequirement were determined at various values of radius of loading head.

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

Szmidla J., Jurczyńska A.

Machine Dynamics Research

2014

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.