Harmonic Wave in Disturbed System of Periodic Elastic Layers
The system of elastic layers periodic in space is considered. One extra cell situated between the cells of numbers k and k + 1 disturbs the system. Harmonic wave of frequency w propagates across the layers. The transparency of the system is defined as the ratio of the transmitted energy flux to the incident energy flux. Transparency depends on the position of the extra layer. The analytic expression for the transparency is given. Transparency is a periodic function of the position of the extra cell, and in general, a non-periodic function of ω. Assuming that the probability of finding the extra layer at the position k is given, the average transparency and its standard deviation has been calculated.
W.M. EWING, W. JARDETZKY and F. PRESS, Elastic waves in layered media, Me Graw-Hill, New York 1957.
G. HERRMANN and M. HERRMANN, Plane strain surface waves in layered half space, J. Non-Linear Mech., 15, 497-503, 1980.
T.J. DEPTH, G. HERRMANN and R.K. KAUL, Harmonic wave propagation in a periodically layered infinite elastic body. I. Antiplane strain, J. Appl. Mech. Tr. ASME, 45, 343-349, 1978; II. Plane strain, J. Appl. Mech. Tr. ASME, 46, 113-119, 1979; III. Plane strain, numerical results, J. Appl. Mech. Tr. ASME, 41, 531-537, 1980.
R.A. GROT and J.D. ACHENBACH, Large deformations of a laminated composite, Int. J. Sol. Struct., 6, 641-655, 1970.
G. HERRMANN, Nondispersive wave propagation in a layered composite, Wave Motion, 4, 319-326, 1982.
T.J. DEPTH and G. HERRMANN, An effective dispersion theory for layered composite, J. Appl. Mech., 50, 157-164, 1983.
L.M. BREKHOWSKIKH, Waves in layered media, Academic Press, New York 1981.
F.J. DYSON, The dynamics of a disordered linear chain, Phys. Rev., 92, 6, 1331-1338, 1953.
R. BELLMAN, Dynamics of disordered linear chain, Phys. Rev., 101, 1, 19, 1956.
H. SCHMIDT, Disordered one-dimensional cristals, Phys. Rev., 105, 2, 425-435, 1957.
Z. WESOŁOWSKI, Wave speeds in periodic elastic layers, Arch. Mech., 43, 2-3, 271-286, 1991.
Z. WESOŁOWSKI, Products of the transition matrices governing the dynamics of a set of elastic layers, Bull. Acad. Polon. Sci., Sci. Tech., 39, 3, 381-387, 1991.
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