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

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Sokół K.

tom 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.

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

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Sokół K.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2012

tom 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.