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DYNAMIC MULTI-STRUCTURE IN MODELLING A TRANSITION FLEXURAL WAVE

Part of: Singular integral equations Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  05 December 2014

Alexander B. Movchan ,
Michele Brun ,
Leonid I. Slepyan  and
Gian F. Giaccu
Alexander B. Movchan
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 7ZL, U.K. email abm@liv.ac.uk
Michele Brun
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 7ZL, U.K. Dipartimento di Ingegneria Meccanica, Chimica e dei Materiali, Universitá di Cagliari, Piazza d’Armi, I-09123 Cagliari, Italy email mbrun@unica.it
Leonid I. Slepyan
Affiliation:
School of Mechanical Engineering, Tel Aviv University, PO Box 39040, Ramat Aviv 69978 Tel Aviv, Israel email leonid@eng.tau.ac.il
Gian F. Giaccu
Affiliation:
Dipartimento di Ingegneria Meccanica, Chimica e dei Materiali, Universitá di Cagliari, Piazza d’Armi, I-09123 Cagliari, Italy Department of Architecture, Design and Urban Planning, University of Sassari, Piazza Duomo 6, Alghero, Italy email gf.giaccu@uniss.it
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Abstract

This paper presents a model of a 1D–1D dynamic multi-structure, supporting propagation of a transition wave. It is used to explain the recent phenomenon of the collapse of the San Saba bridge. An analytical model is supplied with illustrative numerical simulations.

MSC classification

Primary: 35Q15: Riemann-Hilbert problems 45E10: Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) 35Q74: PDEs in connection with mechanics of deformable solids

Information

Type
Research Article
Information
Mathematika , Volume 61 , Issue 2 , May 2015 , pp. 444 - 456
Copyright
Copyright © University College London 2014 

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References

Brun, M., Giaccu, G. F., Movchan, A. B. and Movchan, N. V., Asymptotics of eigenfrequencies in the dynamic response of elongated multi-structures. Proc. R. Soc. Lond. Ser. A 468 2012, 378–394, doi:10.1098/rspa.2011.0415.Google Scholar
Brun, M., Movchan, A. B. and Jones, I. S., Phononic band gap systems in structural mechanics: finite slender elastic structures and infinite periodic waveguides. J. Vib. Acous. 135(4) 2013, 041013, doi:10.1115/1.4023819.CrossRefGoogle Scholar
Brun, M., Movchan, A. B., Jones, I. S. and McPhedran, R. C., Bypassing shake, rattle and roll. Phys. World 26(5) 2013, 32–36.CrossRefGoogle Scholar
Brun, M., Movchan, A. B. and Slepyan, L. I., Transition wave in a supported heavy beam. J. Mech. Phys. Solids 61(10) 2013, 2067–2085, doi:10.1016/j.jmps.2013.05.004.CrossRefGoogle Scholar
Ciarlet, P. G., Plates and Junctions in Elastic Multi-Structures: An Asymptotic Analysis, Masson and Springer (Paris and Heidelberg, 1990).Google Scholar
Ciarlet, P. G., Mathematical Elasticity, Vol. II: Theory of Plates (Studies in Mathematics and its Applications), North-Holland (Amsterdam, 1997).Google Scholar
Kozlov, V. A., Maz’ya, V. G. and Movchan, A. B., Asymptotic Analysis of Fields in Multi-Structures, Oxford University Press (Oxford, 1999).CrossRefGoogle Scholar
Le Dret, H., Problèmes Variationnels dans les Multi-domaines: Modèlisation des Jonctions et Applications, Masson (Paris, 1991).Google Scholar
Mishuris, G. S., Movchan, A. B. and Slepyan, L. I., Localised knife waves in a structured interface. J. Mech. Phys. Solids 57(12) 2009, 1958–1979, doi:10.1016/j.jmps.2009.08.004.CrossRefGoogle Scholar
Panasenko, G. P., Multi-Scale Modelling for Structures and Composites, Springer (Dordrecht, 2005), doi:10.1007/1-4020-2982-9.Google Scholar
Slepyan, L. I., Models and Phenomena in Fracture Mechanics, Springer (Berlin, 2002).CrossRefGoogle Scholar