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Analysis and comparison of several component mode synthesis methods on one-dimensional domains. (English) Zbl 0686.34026
Component mode synthesis methods enable to compute the eigenpairs of a differential operator on a domain that can be subdivided in different subdomains on each of which the eigenpairs of the same operator are assumed to be partially known. Error estimates are given for several of these methods applied to second order elliptic operators on one- dimensional domains. They are partly tied to an argument which is called here “asymptotic hidden regularity” of eigenfunctions of an elliptic operator.
Reviewer: F.Bourquin

34L05 General spectral theory of ordinary differential operators
35P20 Asymptotic distributions of eigenvalues in context of PDEs
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
Full Text: DOI EuDML
[1] Babuska, I., Osborn, J.: Eigenvalue problems. In: Handbook of Numerical Analysis (Ciarlet, P.G., Lions, J.L. (ed.)) vol II. North-Holland, Amsterdam (to appear)
[2] Benfield, W.A., Hruda, R.F.: Vibration analysis of structures by component mode substitution. AIAA J.9 (7) 1255-1261 (1971) · Zbl 0214.23802 · doi:10.2514/3.49936
[3] Bernadou, M., Fayolle, S., Lene, F.: Numerical analysis of junctions between plates. Rapport I.N.R.I.A. n0 865, juillet 1988
[4] Bourquin, F.: Synth?se modale d’op?rateurs elliptiques du second ordre. C.R. Acad. Sci. Paris, S?r. I,309, 919-922 (1989) · Zbl 0685.47038
[5] Bourquin, F.: Domain decomposition and eigenvalues of second order operators: convergence analysis. J. Math. Pures. Appl. 1990 (submitted) · Zbl 0765.65100
[6] Bourquin, F., Ciarlet, P.G.: Mod?lisation des vibrations d’une multi-structure form?e d’un corps ?lastique tridimensionnel et d’une plaque. C.R. Acad. Sci. Paris, S?r. I,307, 435-438 (1988) · Zbl 0659.73049
[7] Bourquin, F., Ciarlet, P.G., Gruais, I.: Junctions between plates and rods: the eigenvalue problem (in preparation)
[8] Ciarlet, P.G.: A justification of the Von Karman equations. Arch. Kat. Mech. Anal.73, 349-389 (1980) · Zbl 0443.73034
[9] Ciarlet, P.G., Le Dret, H., Nzengwa, R.: Mod?lisation de la jonction entre un corps ?lastique tridimensionnel et une plaque. C. R. Acad. Sci. Paris, S?r. I,305, 55-58 (1987) · Zbl 0632.73015
[10] Ciarlet, P.G., Schultz, M.H., Varga, R.S.: Numerical methods of high-order accuracy for non-linear boundary value problems, III: Eigenvalue problems. Numer. Math.12, 120-133 (1968) · Zbl 0181.18303 · doi:10.1007/BF02173406
[11] Courant, R., Hilbert, D.: Methods of mathematical Physics, Vol. 2. New York: Interscience 1953 · Zbl 0051.28802
[12] Craig, R.R.Jr.: A review of time domain and frequency domain component mode synthesis methods, joint ASCE/ASME mechanics conference, Albuquerque, New Mexico, June 24-26, A.M.D. vol. 67, 1985
[13] Craig, R., Bampton, M.C.C.: Coupling of substructures for dynamic analysis. AIAA J.6, 1313-1321 (1968) · Zbl 0159.56202 · doi:10.2514/3.4741
[14] Dunford, N., Schwartz, J.: Linear Operators. New York: Interscience, Wiley 1963 · Zbl 0128.34803
[15] Destuynder, P.: Remarks on dynamic substructuring. Eur. J. Mech. SOLIDS8, 201-218 (1989) · Zbl 0692.73059
[16] Gladwell, B.M.L.: Branch mode analysis of vibrating systems. J. Sound Vib.1, 41-59 (1964) · Zbl 0124.39303 · doi:10.1016/0022-460X(64)90006-9
[17] Goldman, R.L.: Vibration analysis of dynamic partitioning. AIAA J.7, 1152-1154 (1969) · Zbl 0179.55102 · doi:10.2514/3.5290
[18] Hurty, W.C.: Dynamic analysis of structural systems using component modes. AIAA J.4, 678-685 (1965)
[19] Imbert, J.F.: Calcul des structures par ?l?ments finis, cours de l’ENSAE. Toulouse C?padues, 1979
[20] Jezequel, L.: Synth?se modale: th?orie et extensions. Th?se d’?tat, universit? Claude Bernard, 1985
[21] Le Dret, H.: Mod?lisation d’une plaque pli?e. C.R. Acad. Sci. Paris, S?r. I,305, 571-573 (1987) · Zbl 0634.73047
[22] Le Dret, H.: Modeling of, the junction between two rods. J. Math. Pures Appl.68, 365-397 (1989) · Zbl 0743.73020
[23] Lions, J.L.: Contr?labilit? exacte, perturbations et stabilisation des syst?mes distribu?s, tome 1. RMA, Masson, 1988
[24] Lions, J.L., Magenes, E.: Probl?mes aux limites non homog?nes et applications, vol. 1, Paris: Dunod 1968 · Zbl 0165.10801
[25] Mac Neal, R.H.: A hybrid method of component mode synthesis. Comput. Struct.,1, 581-601 (1971) · doi:10.1016/0045-7949(71)90031-9
[26] Morand, H.: M?thodes de d?termination approach?e des modes propres de vibration en calcul des structures; sous-structuration dynamique. ONERA R.T.2, 13238, RY OOOR (1977)
[27] Morand, H., Ohayon, R.: Substructure variational analysis of the vibrations of coupled fluid-structure systems. Finite element. Int. J. Numer. Methods Eng.14, 741-755 (1979) · Zbl 0402.73052 · doi:10.1002/nme.1620140508
[28] Rubin, S.: Improved component mode representation for structural dynamic analysis AIAA J.13, 995-1006 (1975) · Zbl 0334.70014 · doi:10.2514/3.60497
[29] Taylor, A.E.: Introduction to Functional Analysis. New York: Wiley 1958 · Zbl 0081.10202
[30] Valid, R.: Une m?thode de calcul des structures au flambage par sous-structuration et synth?se modale. C. R. Acad. Sci. Paris, Ser. II294, 299-302 (1982) · Zbl 0485.73032
[31] Weinberger, H.: Variational Methods for Eigenvalue Approximations. SIAM, Philadelphia, 1974 · Zbl 0296.49033
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