TY - JOUR

T1 - Transition wave in a supported heavy beam

AU - Brun, Michele

AU - Movchan, Alexander B.

AU - Slepyan, Leonid I.

N1 - Funding Information:
This paper was partially written when L.S. and A.B.M. were Visiting Professors at Cagliari University under the 2011 program funded by Regione Autonoma della Sardegna. L.S. and A.B.M. are also thankful for the support provided by EU-FP7 Grant no. IAPP-2011-284544-PARM-2 and No. PIAP-GA-2011-286110-INTERCER2 . M.B. acknowledges the support of the EU FP7 Grant no. PIEF-GA-2011-302357-DYNAMETA and of the project CRP. 27585 funded by RAS. We particularly thank Dr. Eng. F. Giaccu for the estimation of the geometric parameters of the Millau viaduct.

PY - 2013/10

Y1 - 2013/10

N2 - 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.

AB - 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.

KW - Flexural waves

KW - Fracture

KW - Lattice system

KW - Phase transition

KW - Wiener-Hopf functional equations

UR - http://www.scopus.com/inward/record.url?scp=84880919656&partnerID=8YFLogxK

U2 - 10.1016/j.jmps.2013.05.004

DO - 10.1016/j.jmps.2013.05.004

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AN - SCOPUS:84880919656

SN - 0022-5096

VL - 61

SP - 2067

EP - 2085

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

IS - 10

ER -