Traction, deformation and velocity of deformation in a viscoelastic string

TL;DR

This paper investigates the controllability and relations between traction, deformation, and velocity in a viscoelastic string, revealing similarities to elastic behavior and new phenomena in traction-deformation interactions.

Contribution

It demonstrates that while traction and velocity behave like in elastic cases, traction and deformation exhibit flexible relations allowing arbitrary Fourier component assignments over time.

Findings

Traction and velocity are independent over large times.

Traction and deformation are related but not strictly constrained.

Multiple Fourier components of traction and deformation can be independently controlled.

Abstract

In this paper we consider a viscoelastic string whose deformation is controlled at one end. We study the relations and the controllability of the couples traction/velocity and traction/deformation and we show that the first couple behaves very like as in the purely elastic case, while new phenomena appears when studying the couple of the traction and the deformation. Namely, while traction and velocity are independent (for large time), traction and deformation are related at each time but the relation is not so strict. In fact we prove that an arbitrary number of "Fourier" components of the traction and, independently, of the deformation can be assigned at any time.