The Instability Mechanism of a Confined Rod Under Axial Vibrations

We studied the stability of a confined rod under axial vibrations through a combination of analytical and numerical analysis. We find that the stability of the system is significantly different than in the static case and that both the frequency and magnitude of the applied vibrational force play an important role. In particular, while larger vibrational forces always tend to destabilize the system, our analysis indicates that the effect of the frequency is not obvious and monotonic. For certain frequencies, a very small force is sufficient to trigger an instability, while for others the rod is stable even for large forces. Furthermore, we find that the stability of the confined rod is significantly enhanced by the presence of frictional contact and that in this case also the magnitude of the perturbation affects its response.