Issue 29

G. Carta et alii, Frattura ed Integrità Strutturale, 29 (2014) 28-36; DOI: 10.3221/IGF-ESIS.29.04 36 The results of this work can be used in the context of Structural Health Monitoring for the detection of cracks, defects and imperfections in structural elements. Moreover, they can be exploited to design filtering systems with appropriate discontinuities that can stop the transmission of waves of specified frequencies. It remains a big challenge to study analytically the dynamic properties of solids with randomly-distributed cracks or defects. R EFERENCES [1] Movchan, A.B., Slepyan, L.I., Band gap Green's functions and localized oscillations, Proc. R. Soc. A, 463 (2007) 2709- 2727. [2] Poulton, C.G., Movchan, A.B., Movchan, N.V., McPhedran, R.C., Analytic theory of defects in periodically structured elastic plates, Proc. R. Soc. A, 468 (2012) 1196-1216. [3] Mishuris, G.S., Movchan, A.B., Slepyan, L.I., Localization and dynamic defects in lattice structures, in: V.V. Silberschmidt (Ed.), Computational and experimental mechanics of advanced materials (CISM Courses and Lectures), Vol. 514, Springer, Wien, (2009) 51-82. [4] Bigoni, D., Guenneau, S., Movchan, A.B., Brun, M., Elastic metamaterials with inertial locally resonant structures: application to lensing and localization, Phys. Rev. B, 87 (2013) 174303. [5] Carta, G., Jones, I.S., Brun, M., Movchan, N.V., Movchan, A.B., Crack propagation induced by thermal shocks in structured media, Int. J. Solids Struct., 50 (2013) 2725-2736. [6] Mishuris, G.S., Movchan, A.B., Bercial, J.P., Asymptotic analysis of Bloch-Floquet waves in a thin bi-material strip with a periodic array of finite-length cracks, Waves Random Complex Media, 17 (2007) 511-533. [7] Vellender, A., Mishuris, G.S., Movchan, A.B., Weight function in a bimaterial strip containing an interfacial crack and an imperfect interface. Application to Bloch-Floquet analysis in a thin inhomogeneous structure with cracks, Multiscale Model. Simul., 9 (2011) 1327-1349. [8] Vellender, A., Mishuris, G.S., Eigenfrequency correction of Bloch-Floquet waves in a thin periodic bi-material strip with cracks lying on perfect and imperfect interfaces, Wave Motion, 49 (2012) 258-270. [9] Zalipaev, V.V., Movchan, A.B., Jones, I.S., Two-parameter asymptotic approximations in the analysis of a thin solid fixed on a small part of its boundary, Q. J. Mech. Appl. Math., 60 (2007) 457-471. [10] Gei, M., Jones, I.S., Movchan, A.B., Junction conditions for cracked elastic thin solids under bending and shear, Q. J. Mech. Appl. Math., 62 (2009) 481-493. [11] Carta, G., Brun, M., Movchan, A.B., Dynamic response and localization in strongly damaged waveguides, Proc. R. Soc. A, 470 (2014) 20140136. [12] Dimarogonas, A.D., Vibration of cracked structures: A state of the art review, Eng. Fract. Mech., 55 (1996) 831-857. [13] Ostachowicz, W.M., Krawczuk, M., Analysis of the effect of cracks on the natural frequencies of a cantilever beam, J. Sound Vib., 150 (1991) 191–201. [14] Chondros, T.G., Dimarogonas, A.D., Yao, J., Vibration of a beam with a breathing crack, J. Sound Vib., 239 (2001) 57-67. [15] Mead, D.J., Wave propagation and natural modes in periodic systems: I. Mono-coupled systems, J. Sound Vib., 40 (1975) 1–18. [16] Brun, M., Giaccu, G.F., Movchan, A.B., Movchan, N.V., Asymptotics of eigenfrequencies in the dynamic response of elongated multi-structures, Proc. R. Soc. A, 468 (2012) 378-394. [17] Ciarlet, P.G., Mathematical Elasticity Volume II: Theory of Plates, first ed., North-Holland, Amsterdam, (1997). [18] Pestel, E.C., Leckie, F.A., Matrix methods in elastomechanics, first ed., McGraw-Hill, New York, (1963). [19] Faulkner, M.G., Hong, D.P., Free vibrations of mono-coupled periodic system, J. Sound Vib., 99 (1985) 29–42. [20] Lekner, J., Light in periodically stratified media, J. Opt. Soc. Am. A, 11 (1994) 2892–2899. [21] Romeo, F., Luongo, A., Invariants representation of propagation properties for bi-coupled periodic structures, J. Sound Vib., 257 (2002) 869–886.