caa a22 4500 467947872 CHVBK 20180405193739.0 cr unu---uuuuu 170328e20050301xx s 000 0 eng 10.1007/BF02637036 doi (NATIONALLICENCE)springer-10.1007/BF02637036 (NATIONALLICENCE)springer-10.1007/s00419-004-0358-1 Lower-dimensional long wave dynamic models for idealised fibre-reinforced elastic structures [Elektronische Daten] [L. Kossovitch, R. Moukhomodiarov, G. Rogerson] Summary: The dispersion of harmonic waves in an idealised fibre-reinforced elastic layer is investigated. Guided by a numerical and asymptotic long-wave investigation of the dispersion relation, appropriate scales are introduced to help elucidate features of long wave high- and low-frequency motion. In the former case, the stress-strain-state is determined in terms of the long-wave amplitude, appropriate leading-order and refined second-order governing equations being obtained from the second- and third-order problems, respectively. At each order the dispersion relation associated with the governing equation agrees with the appropriate expansion of the "exact” dispersion relation. With respect to low-frequency motion, the long wave limit of anti-symmetric motion is non-zero. This contrasts with the classical case and also indicates that inextensible fibres preclude classical bending. The asymptotic long-wave low frequency stress-strain-state is determined in terms of the governing extensions and mid-surface deflection in the symmetric and anti-symmetric cases, respectively. Appropriate leading and second-order governing equations are also found for these functions. The second-order equations act both to refine the stress-strain-state and also provide the leading-order governing equation in the vicinity of the appropriate quasi wave front. This phenomenon is illustrated by considering a problem concerning shock edge loading of a semi-infinite layer. Springer-Verlag, 2005 Kossovitch L. Department of Mathematical Theory of Elasticity and Biomechanics, Saratov State University, Astrakhanskaya Str. 83, 410601, Saratov, Russia aut Moukhomodiarov R. Department of Mathematical Theory of Elasticity and Biomechanics, Saratov State University, Astrakhanskaya Str. 83, 410601, Saratov, Russia aut Rogerson G. Centre of Applied Mathematics, School of Computing, Science and Engineering, University of Salford, M5 4WT, UK aut Archive of Applied Mechanics Springer-Verlag 74/5-6(2005-03-01), 359-374 0939-1533 74:5-6<359 2005 74 419 https://doi.org/10.1007/BF02637036 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02637036 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kossovitch L. Department of Mathematical Theory of Elasticity and Biomechanics, Saratov State University, Astrakhanskaya Str. 83, 410601, Saratov, Russia aut NATIONALLICENCE 700 1- Moukhomodiarov R. Department of Mathematical Theory of Elasticity and Biomechanics, Saratov State University, Astrakhanskaya Str. 83, 410601, Saratov, Russia aut NATIONALLICENCE 700 1- Rogerson G. Centre of Applied Mathematics, School of Computing, Science and Engineering, University of Salford, M5 4WT, UK aut NATIONALLICENCE 773 0- Archive of Applied Mechanics Springer-Verlag 74/5-6(2005-03-01), 359-374 0939-1533 74:5-6<359 2005 74 419 NATIONALLICENCE 700 1- Kossovitch L.Yu Department of Mathematical Theory of Elasticity and Biomechanics, Saratov State University, Astrakhanskaya Str. 83, 410601, Saratov, Russia aut NATIONALLICENCE 700 1- Moukhomodiarov R.R. Department of Mathematical Theory of Elasticity and Biomechanics, Saratov State University, Astrakhanskaya Str. 83, 410601, Saratov, Russia aut NATIONALLICENCE 700 1- Rogerson G.A. Centre of Applied Mathematics, School of Computing, Science and Engineering, University of Salford, M5 4WT, UK aut NATIONALLICENCE 856 40 https://doi.org/10.1007/s00419-004-0358-1 text/html Onlinezugriff via DOI Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE NATIONALLICENCE NL-springer