Non-holonomic constraints inducing flutter insability in structures under conservative loadings

TL;DR

This paper demonstrates that non-holonomic constraints can induce flutter and other dynamic instabilities in structures under conservative loads, challenging the common belief that such instabilities require non-conservative forces.

Contribution

It reveals that non-holonomic constraints alone can cause flutter and related instabilities in conservative systems, expanding understanding of structural dynamic behavior.

Findings

Non-holonomic constraints can induce flutter in conservative structures.

Dynamic instabilities can lead to limit cycles suitable for soft robotics.

Instabilities occur even without non-conservative follower loads.

Abstract

Non-conservative loads of the follower type are usually believed to be the source of dynamic instabilities such as flutter and divergence. It is shown that these instabilities (including Hopf bifurcation, flutter, divergence, and destabilizing effects connected to dissipation phenomena) can be obtained in structural systems loaded by conservative forces, as a consequence of the application of non-holonomic constraints. These constraints may be realized through a `perfect skate' (or a non-sliding wheel), or, more in general, through the slipless contact between two circular rigid cylinders, one of which is free of rotating about its axis. The motion of the structure produced by these dynamic instabilities may reach a limit cycle, a feature that can be exploited for soft robotics applications, especially for the realization of limbless locomotion.