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The Stability of Geometrically Nonlinear Column Loaded by a Generalized Force Directed to Positive Pole at Stepped Variable of Flexural Rigidity

Szmidla J., Cieślińska-Gąsior I., Wiktorowicz J.

Machine Dynamics Research

2014

Vol. 38, No. 1

65-72

The results of theoretical and numerical research that aims at determining areas of local and global instability of geometrically non-linear column loaded by a generalized force directed towards a positive pole at stepped variable of flexural rigidity are presented in the paper. Taking into account total potential energy of column, equations of transverse displacements and boundary conditions necessary to solve the issue were obtained. On the basis of the static criterion of stability an influence of variable flexural stiffness and geometrical and physical parameters of system on the value of the bifurcation load of considered structure was determined. The results of numerical calculations were referred to value of critical load of relevant linear column (a comparative column).

On influence of concentraced mass on instability and vibration of a column subjected to Euler's load

Sokół K.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2012

Vol. 11, nr 2

93-101

In this paper, the results of numerical studies on vibration and instability of a geometrically nonlinear column subjected to Euler's load are presented. The system is loaded by external axial force P applied at the free end of the column. Additional concentrated mass is localised on one of column's rods. The Hamilton principle was used to formulate the boundary problem. Due to the geometrical nonlinearity, the solution of the problem was performed by means of the small parameter method. The main purpose of this paper is to investigate an influence of the concentrated mass on divergence instability and critical loading and natural vibration frequency.

The local and global instability and vibration of a nonlinear column subjected to Euler's load

Sokół K.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2010

Vol. 9, nr 1

187-194

In this paper, the results of numerical studies on the local and global instability and vibration of a geometrically nonlinear column subjected to Euler's load are presented. The Hamilton principle was used to formulate the boundary problem. Due to the geometrical nonlinearity, the solution of the problem was performed by means of the perturbation method. The magnitude of the bifurcation load of the nonlinear column, the local and global instability regions and characteristic curves have also been presented.