Traction, deformation and velocity of deformation in a viscoelastic string
This work provides theoretical insights into the controllability of viscoelastic strings, which is relevant for applications in materials science and engineering, but the results are incremental.
The paper studies the relations and controllability of traction, velocity, and deformation in a viscoelastic string, showing that traction and velocity behave similarly to the elastic case, while traction and deformation exhibit a looser relation where arbitrary Fourier components can be independently assigned.
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.