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On the Stability of Columns as Part of Constructions

Bogacz R., Frischmuth K.

Machine Dynamics Problems

2007

Vol. 31, No. 2

13-24

We extend the results of a previous paper on the stability of columns under follower loads. For Beck's boundary conditions, we present new optimal profile functions as well for the continuous as for the piecewise constant case. Next, we test the optimally shaped column by dynamical simulation for stability under disturbed conditions. In particular, we introduce small variations of the profile itself, the type of follower force and the axial load.

Effect of a rotational spring support on the stability of a column with internal damping

Przybylski J.

Vibrations in Physical Systems

2004

Vol. 21

315--318

This work concerns the problem of stability of a geometrically non-linear damped column loaded by a partially follower force. One end of the column is supported by a rotational spring of stiffness, which can be changed as a function of the external load. The loss of stability of such system is of flutter or divergence type what depends on the values of spring rigidity and follower parameter. The limit of stability has been established on the basis of kinetic criterion. For a nonconservative system an adjoint problem has been formulated. Lyapunow stability criterion has been complemented by Suguyama consideration concerning the time of achieving of demanded displacement by a chosen point on the vibrating column.