Uniform stability in structural acoustic models with flexible curved walls

Abstract The aim of this paper is twofold. First, we develop an explicit extension of the Kirchhoff model for thin shells, based on the model developed by Michel Delfour and Jean-Paul Zolesio. This model relies heavily on the oriented distance function which describes the geometry. Once this model is established, we investigate the uniform stability of a structural acoustic model with structural damping. The result no longer requires that the active wall be a plate. It can be virtually any shell, provided that the shell is thin enough to accommodate the curvatures.

[1]  C. Fuller,et al.  Piezoelectric Actuators for Distributed Vibration Excitation of Thin Plates , 1991 .

[2]  Michel C. Delfour,et al.  Differential equations for linear shells: Comparison between intrinsic and classical models , 1997 .

[3]  G. Whitham.  Research in Applied Mathematics. , 1988 .

[4]  Harvey Thomas Banks,et al.  The modeling of piezoceramic patch interactions with shells, plates, and beams , 1995 .

[5]  E. F. Crawley,et al.  Development of Piezoelectric Technology for Applications in Control of Intelligent Structures , 1988, 1988 American Control Conference.

[6]  Richard J. Silcox,et al.  Simultaneous Active Control of Flexural and Extensional Waves in Beams , 1990 .

[7]  Irena Lasiecka,et al.  Exponential stability of a thermoelastic system without mechanical dissipation , 1995 .

[8]  Irena Lasiecka,et al.  Control Theory for Partial Differential Equations: Preface , 2000 .

[9]  Harvey Thomas Banks,et al.  Modeling and Control of Acoustic Structure Interaction Problems Via Piezoceramic Actuators: 2-D Numerical Examples , 1994 .

[10]  M. Delfour,et al.  Tangential Differential Equations for Dynamical Thin/Shallow Shells , 1996 .

[11]  H. T. Banks,et al.  Well-Posedness of a Model for Structural Acoustic Coupling in a Cavity Enclosed by a Thin Cylindrical Shell , 1995 .

[12]  Jacques-Louis Lions,et al.  Modelling Analysis and Control of Thin Plates , 1988 .

[13]  Philippe G. Ciarlet,et al.  Existence theorems for two-dimensional linear shell theories , 1994 .

[14]  J. Lagnese.  Boundary Stabilization of Thin Plates , 1987 .

[15]  Bo Liu,et al.  On the Spectral Properties and Stabilization of Acoustic Flow , 1998, SIAM Journal on Applied Mathematics.

[16]  George Avalos,et al.  THE EXPONENTIAL STABILITY OF A COUPLED HYPERBOLIC/PARABOLIC SYSTEM ARISING IN STRUCTURAL ACOUSTICS , 1996 .

[17]  I. Lasiecka,et al.  Riccati Equations Arising in Acoustic Structure Interactions with Curved Walls , 1998 .

[18]  P. G. Ciarlet,et al.  Sur L’Ellipticite du Modele Lineaire de coques de W.T. Koiter , 1976 .

[19]  E. Crawley,et al.  Use of piezoelectric actuators as elements of intelligent structures , 1987 .

[20]  Michel C. Delfour,et al.  A Boundary Differential Equation for Thin Shells , 1995 .

[21]  Chris R. Fuller,et al.  Active control of propeller-induced noise fields inside a flexible cylinder , 1990 .

[22]  M. Camurdan.  Uniform stabilization of a coupled structural acoustic system by boundary dissipation , 1998 .

[23]  Catherine Lebiedzik.  Uniform stability of a coupled structural acoustic system with thermoelastic effects , 2000 .