Control and stabilization in nonlinear structural acoustic problems

Irena Lasiecka; Rich Marchand

doi:10.1117/12.276538

13 June 1997 Control and stabilization in nonlinear structural acoustic problems

Irena Lasiecka, Rich Marchand

Proceedings Volume 3039, Smart Structures and Materials 1997: Mathematics and Control in Smart Structures; (1997) https://doi.org/10.1117/12.276538
Event: Smart Structures and Materials '97, 1997, San Diego, CA, United States

Abstract

We consider a model arising in structural acoustic problems which is comprised of an acoustic chamber with flexible walls to which piezo-ceramic devices are attached. The deices play the role of actuators and sensors for the model. The mathematical description of the model is governed by a coupled system of partial differential equations involving the wave equation coupled with a nonlinear dynamic shell equation. The main aim is to reduce a pressure/noise in the cabin by the appropriate activation of piezo-ceramic devices. The assumed periodic nature of the disturbance, leads naturally to the formulation of a periodic control problem. This, in turn, is strongly linked to the problem of stabilizability of the original model. Thus, the goal of this paper is to present new results on (i) uniform stabilizability of the structural acoustic model with passive damping applied to the boundary of the acoustic chamber, and (ii) an optimal control problem with 'smart' controls activated by piezo-ceramic patches creating suitable bending moments in the structure. The control algorithm is constructed in a feedback from via a solution of a suitable Riccati type equation. One of our results shows the boundedness of the feedback gains in spite of the strong unboundedness of the control operators. This is due to the 'regularizing' effects of shell dynamics which are partially propagated into the 'hyperbolic' component of the structure.

Citation Download Citation

Irena Lasiecka and Rich Marchand "Control and stabilization in nonlinear structural acoustic problems", Proc. SPIE 3039, Smart Structures and Materials 1997: Mathematics and Control in Smart Structures, (13 June 1997); https://doi.org/10.1117/12.276538

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