Optimization problems for structural acoustic models with thermoelasticity and smart materials

 Access to full text

 Full (PDF)

1. [1] G. Avalos and I. Lasiecka, Differential Riccati equation for the active control of a problem in structural acoustics, JOTA 91 (1996), 695-728. Zbl0869.93023
2. [2] G. Avalos and I. Lasiecka, The strong stability of a semigroup arising from a coupled hyperbolic/parabolic system, Semigroup Forum 57 (1997), 278-292. Zbl0910.35014
3. [3] A.V. Balakrishnan, Applied Functional Analysis, Springer Verlag 1975. Zbl0333.93051
4. [4] H.T. Banks, R.J. Silcox and R.C. Smith, The modeling and control of acoustic/structure interaction problems via piezoceramic actuat ors: 2-D numerical examples, ASME Journal of Vibration and Acoustics 2 (1993), 343-390. 
5. [5] H.T. Banks and R. Smith, Active control of acoustic pressure fields using smart material technology in flow control, IMA, (M. Gunzburger, ed.) 68 Springer Verlag 1995. Zbl0848.73048
6. [6] H.T. Banks and R.C. Smith, Well-Posedness of a model for structural acoustic coupling in a cavity enclosed by a thin cylindrical shell, Journal of Mathematical Analysis and Applications 191 (1995), 1-25. Zbl0824.73048
7. [7] H.T. Banks, R.C. Smith and Y. Wang, The modeling of piezoceramic patch interactions with shells, plates and beams, Quaterly of Applied Mathematics 53, 2 (1995), 353-381. Zbl0832.73061
8. [8] V. Barbu, I. Lasiecka and R. Triggiani, Extended Algebraic Riccati Equations arising in hyperbolic dynamics with unbounded controls, Nonlinear Analysis, to appear. Zbl0961.49003
9. [9] J. Beale, Spectral properties of an acoustic boundary condition, Indiana Univ. Math. J. 9 (1976), 895-917. Zbl0325.35060
10. [10] A. Bensoussan, G. Da Prato, M.C. Delfour and S.K. Mitter, Representation and Control of Infinite Dimensional Systems, vol. II, Birkhauser, Boston 1993. Zbl0790.93016
11. [11] M. Camurdan and R. Triggiani, Control Problems in Noise Reduction: The case of two coupled hyperbolic equations, in: Proceedings of SPIE's 4-th Annual Symposium on Smart Structures and Materials, Mathematic and Control in Smart Structures 1997. Zbl1014.35058
12. [12] M. Camurdan and R. Triggiani, Sharp Regularity of a coupled system of a wave and Kirchhoff equation with point control, arising in noise reduction, Diff and Integral Equations 1998. Zbl1014.35058
13. [13] E.F. Crawley and E. H. Anderson, Detailed models of piezoceramic actuation of beams, in: Proc. of AIAA Conference 1989. 
14. [14] E.F. Crawley and J. de Luis, Use of piezoelectric actuators as elements of intelligent structures, AIAA Journal 25 (1987), 1373-1385. 
15. [15] E.K. Dimitriadis, C.R. Fuller and C.A. Rogers, Piezoelectric Actuators for Distributed Noise and Vibration Excitation of Thin Plates, Journal of Vibration and Acoustics 13 (1991), 100-107. 
16. [16] F. Flandoli, Riccati equations arising in boundary control problems with distributed parameters, SIAM J. Control 22 (1984), 76-86. Zbl0533.49004
17. [17] F. Flandoli, I. Lasiecka and R. Triggiani, Algebraic Riccati Equations with non-smoothing observations arising in hyperbolic and Euler-Bernoulli boundary control problems, Annali di Matematica Pura et. Applicata 153 (1988), 307-382. Zbl0674.49004
18. [18] P. Grisvard, Characterization de quelques espaces d'interpolation, Archive rational Mechanics and Analysis 26 (1967), 40-63. Zbl0187.05901
19. [19] I. Lasiecka, NSF-CBMS Lecture Notes on Mathematical Control Theory of Coupled PDE's, SIAM, Philadelphia 2000. 
20. [20] J. Lagnese, Boundary Stabilization of Thin Plates, SIAM, Philadelphia 1989. 
21. [21] I. Lasiecka, Mathematical control theory in structural acoustic problems, Mathematical Models and Methods in Applied Sciences 8 (1998), 1119-1153. Zbl0940.93037
22. [22] I. Lasiecka, Boundary stabilization of a 3-dimensional structural acoustic model, Journal de Math. Pure et Appli. 78 (1999), 203-232. Zbl0927.35060
23. [23] I. Lasiecka, Uniform decay rates for full von Karman system of dynamic elasticity with free boundary conditions and partial boundary dissipation, Communications in PDE 24 (1999), 1801-1849. Zbl0934.35195
24. [24] I. Lasiecka and C. Lebiedzik, Decay rates in nonlinear structural acoustic models with thermal effects and without a damping on the interface, Preprint, 1999. Zbl0960.93020
25. [25] I. Lasiecka and C. Lebiedzik, Boundary stabilizability of nonlinear structural acoustic models with thermal effects on the interface, C.R. Acad. Sci. Paris, serie II b, (2000), 1-6. Zbl0982.93062
26. [26] I. Lasiecka and R. Triggiani, Differential and Algebraic Riccati Equations with Applications to Boundary/Point Control Problems, Continuous Theory and Approximation Theory, Springer Verlag, LNCIS 164, 1991. Zbl0754.93038
27. [27] I. Lasiecka and R. Triggiani, Riccati differential equations with unbounded coefficients and nonsmooth terminal condition-the case of analytic semigroups, SIAM J. Math. Analysis 23 (2) (1992), 448-481. Zbl0774.34047
28. [28] I. Lasiecka and R. Triggiani, Analyticity and lack thereof, of thermoelastic semigroups, ESAIM 4 (1998), 199-222. Zbl0906.35018
29. [29] I. Lasiecka and R. Triggiani, Analyticity of thermo-elastic semigroups with free B.C., Annali di Scuola Normale Superiore XXVII (1998), 457-482. Zbl0954.74029
30. [30] I. Lasiecka and R. Triggiani, Two direct proofs on the analyticity of the S.C. semigroup arising in abstract thermo-elastic equations, Advances in Differential Equations 3 (1998), 387-416. Zbl0949.35135
31. [31] I. Lasiecka and R. Triggiani, Control Therory for Partial Differential Equations, Cambridge University Press, Cambridge 1999. 
32. [32] C. Lebiedzik, Exponential stability in structural acoustic models with thermoelasticity, Dynamics of Continous, Discrete and Impulsive Systems, 1999. 
33. [33] H.C. Lester and C.R. Fuller, Active control of propeller induced noise fields inside a flexible cylinder, in: Proc. of AIAA Tenth Aeroacoustics Conference, Seattle, WA 1986. 
34. [34] J.L. Lions and E. Magenes, Non-homogenous Boundary Value Problems and Applications, Springer Verlag, New York 1972. 
35. [35] Z. Liu and M. Renardy, A note on the equation of thermoelastic plate, Applied Math. Letters 8 (1995), 1-6. Zbl0826.35048
36. [36] P.M. Morse and K.U. Ingard, Theoretical Acoustics, McGraw-Hill, New York 1968. 
37. [37] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, New York 1986. 
38. [38] G. Da Prato, I. Lasiecka and R. Triggiani, A Direct Study of Riccati Equations arising in Hyperbolic Boundary Control Problems, Journal of Differential Equations 64 (1986), 26-47. Zbl0601.49003
39. [39] D.L. Russell, Controllability and stabilizability theory for linear partial differential equations. recent progress and open questions, SIAM Review 20 (1978), 639-739. Zbl0397.93001
40. [40] D.L. Russell, Mathematical models for the elastic beam and their control-theoretic properties, Semigroups Theory and Applications, Pitman Research Notes 152 (1986), 177-217. 
41. [41] R. Triggiani, Lack of exact controllability for wave and plate equations with finitely many boundary controls, Differential and Integral Equations 4 (1991), 683-705. Zbl0743.35039
42. [42] R. Triggiani, Interior and boundary regularity of the wave equation with interior point control, Differential and Integral Equations 6 (1993), 111-129. Zbl0786.35086
43. [43] R. Triggiani, Regularity with interior point control, part II: Kirchhoff equations, Journal of Differential Equations 103 (1993), 394-420. Zbl0800.93596
44. [44] R. Triggiani, The Algebraic Riccati Equations with Unbounded Coefficients; Hyperbolic Case Revisited, Contemporary Mathematics: Optimization Methods in PDE's, AMS, Providence 209 (1997), 315-339. 
45. [45] R. Triggiani, Sharp regularity of thermoelastic plates with point controls, Abstract and Applied Analysis, to appear. 
46. [46] M. Tucsnak, Control of plates vibrations by means of piezoelectric actuators, Discrete and Continuous Dynamical Systems 2 (1996), 281-293. Zbl0965.93068
47. [47] G. Weiss and H. Zwart, An example in LQ optimal control, Systems and Control Letters 33 (1998), 339-349. Zbl0901.49028