ANALYSIS OF A HYBRID SYSTEM FOR NOISE REDUCTION

摘要

We consider a simple model arising in the control of noise. We assume that the two-dimensional cavity Ω = (0,1) × (0,1) is occupied by an elastic, inviscid, compressible fluid. The potential Φ of the velocity field satisfies the linear wave equation. The boundary of Ω is divided into two parts Γ_0 and Γ_1. The first one, Γ_0, is flexible and occupied by a Bernoulli-Euler beam. On Γ_0 the continuity of the normal velocities of the fluid and the beam is imposed. The subset Γ_1 of the boundary is assumed to be rigid and therefore, the normal velocity of the fluid vanishes. We analyse the possibility of changing the dynamics of the system by acting only on the flexible part of the boundary. The problems of stabilization, control and existence of periodic solutions are considered (the damping term, the control and the periodic non-homogeneous term respectively acting on Γ_0).