Stabilization of a nonlinear structural acoustic interaction

Abstract

We consider a structural-acoustic wall problem in dimension 3, in which the structural wall is modeled by a 2D Kirchhoff-Boussinesq plate and acoustic medium subject to a boundary damping. The structure subjected to: a nonlinear external forces [Boussinesq] which may lead to blow up of solutions, and the restoring internal forces mitigating the blow up. It will be shown that a suitable calibration between the forces and boundary damping, subject to certain geometric configurations, leads to a wellposed nonlinear control system. For such system, feedback stabilization of solutions [both strong and uniform] is established. The main difficulties and novelty encountered in the problem are the following: (i) the nonlinear effects are not locally Lipschitz, (ii) the system is not dissipative and (iii) the presence of un-observed Neumann data on the interface. To handle these difficulties new methods in dynamical systems and geometric analysis are developed and applied.

Publication Title

Proceedings of the American Control Conference

Link to Full Text

Share

COinS