Effects of Geometric Nonlinearities on the Dynamic Characteristics of Portal Frames

Resumo

In this paper, we present a study of the effects of the presence of large compressive axial forces applied
to members of portal frames on their vibration frequencies. It is a well-known fact that axial forces in structural
members may affect the so-called geometric stiffness. If they are compressive, the overall stiffness will decrease,
and, as a consequence, the vibration frequencies also.
Our structural model is a simple portal frame composed of two upright columns fixed at their bases supporting a
horizontal beam pinned at both ends. We suppose a motor to be mounted at the beam mid span. The natural
frequencies of vibration of the structure will usually be set far away from the machine nominal operational speed
to avoid possible resonance due to motor unbalance. But if large axial forces are applied to the portal frame
members changing their geometric stiffness and frequencies, unexpected resonances may occur, potentially
dangerous.
Two analysis are carried out. First, a simplified mathematical model is derived using simple Rayleigh’s Method
considerations. Next, a more refined Finite Element model is implemented. Results agree reasonably well.