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Turbe, Nicole

Bloch waves for a solid-fluid mixture. (English) Zbl 0542.73063

Ann. Fac. Sci. Toulouse, V. Sér., Math. 6, 87-101 (1984).
See the preview in Zbl 0525.73025.

Cited in 1 Document

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74H45 Vibrations in dynamical problems in solid mechanics
76A02 Foundations of fluid mechanics
49R50 Variational methods for eigenvalues of operators (MSC2000)
47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
74E10 Anisotropy in solid mechanics

Keywords:

vibrations of unbounded, periodic, mixture of elastic solid and viscous compressible fluid; equations of motion; expansion in terms of Bloch waves; approximations; connection with homogeneization theory

Citations:

Zbl 0525.73025
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\textit{N. Turbe}, Ann. Fac. Sci. Toulouse, Math. (5) 6, 87--101 (1984; Zbl 0542.73063)
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References:

[1] Achenbach, J.D.. «Waves and vibrations in directionally reinforced composites». Composite materials, vol. 2, Mechanics of composite materials L.J. Broutman, R.M. Kroch (ed.). Academic Press, New-York (1975), pp. 309-351.
[2] Bensoussan, A., Lions, J.L., Papanicolaou, G.. «Asymptotic analysis for periodic structures». North-Holland, Amsterdam (1978). · Zbl 0404.35001
[3] Delph, T.J., Herrmann, G., Kaul, R.K.. «Harmonic wave propagation in a periodically layered, infinite elastic body, antiplane strain». J. Appl. Mech., 45 (1978), pp. 343-349.
[4] Sanchez-Hubert, J.. «Asymptotic study of the macroscopic behaviour of a solidfluid mixture». Math. Meth. Appl. Sci., 2 (1980) pp. 1-11. · Zbl 0427.73025
[5] Sanchez-Palencia, E.. «Non-homogeneous media and vibration theory». Springer, Berlin (1980). · Zbl 0432.70002
[6] Sun, C.T., Achenbach, J.D., Herrmann, G.. «Continuum theory foralaminated medium». J. Appl. Mech.35 (1968), pp. 467-473. · Zbl 0177.54303
[7] Sve, C.. «Time harmonic waves traveling obliquely in a periodically laminated medium». J. Appl. Mech.38 (1971), pp. 477-482.
[8] Turbe, N.. «Applications of Bloch expansion to periodic elastic and viscoelastic media». Math. Meth. Appl. Sci.4 (1982) pp. 433-449. · Zbl 0495.73014
[9] Turbe, N.. Thèse de Doctorat, Université Pierre et Marie Curie (1982).
[10] Turbe, N.. Communication colloque du Groupe Français de Rhéologie (1982).
[11] Wilcox, C.H.. «Theory of Bloch waves». J. Anal. Math.33 (1978) pp. 146-167. · Zbl 0408.35067
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