Journal of Theoretical
and Applied Mechanics

45, 4, pp. 873-892, Warsaw 2007

Free vibrations and stability of discrete systems subjected to the specific load

Lech Tomski, Janusz Szmidla
In this paper, we present discrete systems subjected to a generalised specific load by a force directed towards to positive pole and a follower force directed towards the positive pole. The critical load and the course of the natural frequency in relation to the external load are determined. Adequate relationships describing stability of the considered columns are obtained taking into account potential energy of the systems (energetic method) or total mechanical energy (vibration method). Geometrical parameters of heads realising the load and rigidity of rotational springs modelling the finite stiffness of structural constraints of the system are taken into account.
Keywords: discrete slender system; divergence instability; rigid body dynamics; natural frequency