Configurational forces and nonlinear structural dynamics

TL;DR

This paper demonstrates how configurational forces significantly affect the nonlinear dynamics of an elastic rod, confirmed through theoretical modeling and experiments, with potential applications in flexible robotic systems.

Contribution

It extends the understanding of configurational forces from static to dynamic settings and develops a nonlinear dynamic model validated by experiments.

Findings

Configurational forces influence rod dynamics significantly.

Rod exhibits nonlinear oscillatory behavior with slipping in and out of the sleeve.

Experimental results confirm theoretical predictions.

Abstract

Configurational, or Eshelby-like, forces are shown to strongly influence the nonlinear dynamics of an elastic rod constrained with a frictionless sliding sleeve at one end and with an attached mass at the other end. The configurational force, generated at the sliding sleeve constraint and proportional to the square of the bending moment realized there, has been so far investigated only under quasi-static setting and is now confirmed (through a variational argument) to be present within a dynamic framework. The deep influence of configurational forces on the dynamics is shown both theoretically (through the development of a dynamic nonlinear model in which the rod is treated as a nonlinear spring, obeying the Euler elastica, with negligible inertia) and experimentally (through a specifically designed experimental set-up). During the nonlinear dynamics, the elastic rod may slip alternatively in and out from the sliding sleeve, becoming a sort of nonlinear oscillator displaying a motion eventually ending with the rod completely injected into or completely ejected from the sleeve. The present results may find applications in the dynamics of compliant and extensible devices, for instance, to guide the movement of a retractable and flexible robot arm.