Transition wave in a supported heavy beam

Michele Brun*, Alexander B. Movchan, Leonid I. Slepyan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


We consider a heavy, uniform, elastic beam rested on periodically distributed supports as a simplified model of a bridge. The supports are subjected to a partial destruction propagating as a failure wave along the beam. Three related models are examined and compared: (a) a uniform elastic beam on a distributed elastic foundation, (b) an elastic beam in which the mass is concentrated at a discrete set of points corresponding to the discrete set of the elastic supports and (c) a uniform elastic beam on a set of discrete elastic supports. Stiffness of the support is assumed to drop when the stress reaches a critical value. In the formulation, it is also assumed that, at the moment of the support damage, the value of the 'added mass', which reflects the dynamic response of the support, is dropped too. Strong similarities in the behavior of the continuous and discrete-continuous models are detected. Three speed regimes, subsonic, intersonic and supersonic, where the failure wave is or is not accompanied by elastic waves excited by the moving jump in the support stiffness, are considered and related characteristic speeds are determined. With respect to these continuous and discrete-continuous models, the conditions are found for the failure wave to exist, to propagate uniformly or to accelerate. It is also found that such beam-related transition wave can propagate steadily only at the intersonic speeds. It is remarkable that the steady-state speed appears to decrease as the jump of the stiffness increases.

Original languageEnglish
Pages (from-to)2067-2085
Number of pages19
JournalJournal of the Mechanics and Physics of Solids
Issue number10
StatePublished - Oct 2013


FundersFunder number
EU-FP7PIAP-GA-2011-286110-INTERCER2, IAPP-2011-284544-PARM-2
Seventh Framework Programme286110, 302357, 284544
Royal Astronomical Society
Università di Cagliari
Seventh Framework Programme27585, PIEF-GA-2011-302357-DYNAMETA
Regione Autonoma della Sardegna


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    • Fracture
    • Lattice system
    • Phase transition
    • Wiener-Hopf functional equations


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