Dynamic response and localization in strongly damaged waveguides by G. Carta, M. Brun, and A. B. Movchan Proceedings A Volume 470(2167): July 8, 2014 ©2014 by The Royal Society

Railway viaduct in Piacenza, Italy (image taken from accessed on 31 January 2014). G. Carta et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

(a) Example of an elongated damaged structure: rail bridge over Westmoreland Road, Bath, UK (image taken from Google Maps Street View, retrieved on 31 January 2014); (b) schematic of a finite strip with equispaced cracks; (c) eigen... G. Carta et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

(a) Finite elastic strip with equispaced transverse cracks, that consists of five repeating cells; (b) detail of a repetitive cell. G. Carta et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

Eigenfrequencies of finite strips possessing different lengths. G. Carta et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

Dispersion diagrams of the infinite periodic strip for ρ/h=1/5 (a) and ρ/h=1/100 (b), obtained from the finite-element software COMSOL Multiphysics. G. Carta et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

First eight modes (at increasing eigenfrequencies) relative to the standing waves (figure 5b) at k=π/l ((a), (b), (e), (f)) and k=0 ((c), (d), (g), (h)), provided by the finite-element code. G. Carta et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

Periodic cell of a beam with elastic connections. G. Carta et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

Elastic strip subjected to symmetric rotations (a) and antisymmetric displacements (b) at the ends. G. Carta et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

Physical plane representation of the propagation zones. G. Carta et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

Dispersion curves for an intact beam (solid grey lines) and for a damaged beam (solid thick black lines) with ρ=h/5 (a) and ρ=h/100 (b). G. Carta et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

Non-dimensional frequency parameter ϕ versus normalized wavenumber kl for ρ/h=1/5 (a) and ρ/h=1/100 (b). G. Carta et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

Lowest two eigenmodes of simple beams with different boundary conditions. G. Carta et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society

First normalized eigenfrequency, as a function of the corresponding normalized stiffness, of the beams shown in figure 12. G. Carta et al. Proc. R. Soc. A 2014;470: ©2014 by The Royal Society