×

zbMATH — the first resource for mathematics

Theoretical study and optimization of a fluid-structure interaction problem. (English) Zbl 0663.76096
The small harmonic vibrations of an elastoacoustic coupled system are under study. A symmetric variational formulation is presented, which particularly suits the model problem. The mathematical study is derived and the existence of a real spectrum of eigenvalues is proved. Then, the problem of designing the coupled structure such as to obtain as large a gap as possible in the eigenvalues spectrum is considered, in order to avoid resonance for a wide range of external excitation frequencies. An optimally criterion method is applied, using the structure thickness distribution as a control variable.

MSC:
76Q05 Hydro- and aero-acoustics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
49S05 Variational principles of physics (should also be assigned at least one other classification number in Section 49-XX)
35Q99 Partial differential equations of mathematical physics and other areas of application
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] M. A. HAMDI, Y. OUSSET, G. VERCHERY, 1978, A Displacement method for the analysis of vibrations of coupled Fluid-Structure Systems. Int. Journal for Num. Meth. in Eng., vol. 13, n^\circ 1, pp. 139-150. Zbl0384.76060 · Zbl 0384.76060 · doi:10.1002/nme.1620130110
[2] C. FELIPPA, 1986, Some aspects of the Symmetrization of the contained Compressible Fluid-Vibration eigenproblem in Innovating Numerical Methods in Engineering. Springer-Verlag Berlin. Heidelberg. New York. Tokyo. Zbl0595.76069 · Zbl 0595.76069
[3] R. OHAYON, 1979, Formulation variationnellle symétrique du problème des vibrations harmoniques par couplage des principes primal et dual. Application aux oscillations de systèmes couplés fluide-strucutre. La Recherche Aérospatiale, n^\circ 3 (mai-juin), pp. 207-211. Zbl0422.73046 · Zbl 0422.73046
[4] J. BOUJOT, 1986, Mathematical formulation of fluid-structure interactions problems. To appear in M2AN. Zbl0617.73052 MR896242 · Zbl 0617.73052 · eudml:193501
[5] H. BERGER, J. BOUJOT, R. OHAYON, 1975, On a spectral problem in vibration mechanics computation of elastic tanks partially filled with liquids. Journal of Mathematical analysis and applications, 51, pp. 272-298. Zbl0311.73053 MR386456 · Zbl 0311.73053 · doi:10.1016/0022-247X(75)90123-7
[6] R. OHAYON, 1984, Transient and modal analysis of bounded medium fluid-structure Problems. In Numerical Methods for transient and coupled problems. Venice.
[7] G. DUVAUT, J. L. LIONS, 1972, Les inéquations variationnelles en mécanique et en physique. Dunod, Paris. Zbl0298.73001 MR464857 · Zbl 0298.73001
[8] A. C. DENEUVY, 1986, Etude d’un problème de conception optimale avec critère sur les fréquences pour un système couplé fluide-strucutre. Thèse. Ecole Centrale de Lyon.
[9] A. C. DENEUVY, 1987, A new modal synthesis method for a fluid-structure problem. Resolution and Optimization. (To appear).
[10] J. DENY, J. L. LIONS, 1953, Les espaces de type Beppo-Levi. Ann. Inst. Fourier (Grenoble), 5, pp. 305-370. Zbl0065.09903 MR74787 · Zbl 0065.09903 · doi:10.5802/aif.55 · numdam:AIF_1954__5__305_0 · eudml:73718
[11] H. BREZIS, 1983, Analyse fonctionnelle (Théorie et Applications). Masson, Paris. Zbl0511.46001 MR697382 · Zbl 0511.46001
[12] M. P. BENDSOE, N. OLHOFF, 1983, A method of design against vibration resonance of beams and shafts. First IASTED International Symposium on applied control and identification, Copenhagen Denmark, June. Zbl0569.49009 · Zbl 0569.49009 · doi:10.1002/oca.4660060302
[13] N. OLHOFF, R. PLAUT, 1983, Bimodal optimization of vibrating shallow arches. Int. J. structures, vol. 19, n^\circ 5, pp. 663-670. Zbl0511.73098 · Zbl 0511.73098 · doi:10.1016/0020-7683(83)90092-6
[14] N. OLHOFF, 1973, On singularities, Local Optima and Formation of stiffners in optimal design of plates. Report n^\circ 56, September DC. AMN. The technical University of Denmark. Zbl0333.73052 · Zbl 0333.73052
[15] J. E. TAYLOR, M. P. BENDSOE, 1984, An interpretation for Min-Max structural design Problems including a Method for relaxing constraints. Int. J. Solids Structures, vol. 20, n^\circ 4, pp. 301-314. Zbl0531.73062 MR737512 · Zbl 0531.73062 · doi:10.1016/0020-7683(84)90041-6
[16] M. P. BENDSOE, 1984, Existence proofs for a class of plate optimization problems. Lecture notes in Control and Information Sciences, vol. 59, Springer, pp. 773-779). Zbl0542.49002 MR769713 · Zbl 0542.49002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.