Some controllability results for linear viscoelastic fluids

We analyze the controllability properties of systems which provide a description, at first approximation, of a kind of viscoelastic fluid. We consider linear Maxwell fluids. First, we establish the large time approximate-finite dimensional controllability of the system, with distributed or boundary controls supported by arbitrary small sets. Then, we prove the large time exact controllability of fluids of the same kind with controls supported by suitable large sets. The proofs of these results rely on classical arguments. In particular, the approximate controllability result is implied by appropriate unique continuation properties, while exact controllability is a consequence of observability (inverse) inequalities. We also discuss questions concerning the controllability of viscoelastic fluids and some related open problems.Ministerio de Ciencia e Innovació

Vibration characteristics of MR cantilever sandwich beams: experimental study

The concept of vibration controllability with smart fluids within flexible structures has been in the centre of interest in the past two decades. Although much research has been done on structures with embedded electrorheological (ER) fluids, there has been little investigation of magnetorheological (MR) fluid adaptive structures. In particular, a body of research on experimental work of cantilever MR beams is still lacking. This experimental study investigates controllability of vibration characteristics of magnetorheological cantilever sandwich beams. These adaptive structures are produced by embedding an MR fluid core between two elastic layers. The structural behaviour of the MR beams can be varied by applying an external magnetic field to activate the MR fluid. The stiffness and damping structural characteristics are controlled, demonstrating vibration suppression capabilities of MR fluids as structural elements. MR beams were fabricated with two different materials for comparison purposes. Diverse excitation methods were considered as well as a range of magnetic field intensities and configurations. Moreover, the cantilever MR beams were tested in horizontal and vertical configurations. The effects of partial and full activation of the MR beams were outlined based on the results obtained. Controllability of the beam’s vibration response was observed in the form of variations in vibration amplitudes and shifts in magnitudes of the resonant natural frequency

Control problems for weakly coupled systems with memory

We investigate control problems for wave-Petrovsky coupled systems in the presence of memory terms. By writing the solutions as Fourier series, we are able to prove Ingham type estimates, and hence reachability results. Our findings have applications in viscoelasticity theory and linear acoustic theory

Reachability problems for a wave-wave system with a memory term

We solve the reachability problem for a coupled wave-wave system with an integro-differential term. The control functions act on one side of the boundary. The estimates on the time is given in terms of the parameters of the problem and they are explicitly computed thanks to Ingham type results. Nevertheless some restrictions appear in our main results. The Hilbert Uniqueness Method is briefly recalled. Our findings can be applied to concrete examples in viscoelasticity theor