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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/37164

Title: On Boussinesq-type models for long longitudinal waves in elastic rods
Authors: Garbuzov, F.E.
Khusnutdinova, Karima R.
Semenova, I.V.
Keywords: Boussinesq-type models
Longitudinal waves
Elastic rods
Pre-stretch
Solitons
Issue Date: 2019
Publisher: © Elsevier
Citation: GARBUZOV, F.E., KHUSNUTDINOVA, K.R. and SEMENOVA, I.V., 2019. On Boussinesq-type models for long longitudinal waves in elastic rods. Wave Motion, 88, pp.129-143.
Abstract: In this paper we revisit the derivations of model equations describing long nonlinear longitudinal bulk strain waves in elastic rods within the scope of the Murnaghan model in order to derive a Boussinesq-type model, and extend these derivations to include axially symmetric loading on the lateral boundary surface, and longitudinal pre-stretch. We systematically derive two forced Boussinesq-type models from the full equations of motion and non-zero surface boundary conditions, utilising the presence of two small parameters characterising the smallness of the wave amplitude and the long wavelength compared to the radius of the waveguide. We compare the basic dynamical properties of both models (linear dispersion curves and solitary wave solutions). We also briefly describe the laboratory experiments on generation of bulk strain solitary waves in the Ioffe Institute, and suggest that this generation process can be modelled using the derived equations.
Description: This paper is closed access until 20 February 2020.
Sponsor: F.E.G. and I.V.S. acknowledge the financial support from the Russian Science Foundation, Russia under the grant # 17-72-20201. K.R.K. is grateful to the UK Institute of Mathematics and its Applications (IMA) and the QJMAM Fund for Applied Mathematics for the financial support of her travel to the European Solid Mechanics Conference (ESMC2018) in Bologna, Italy in the summer of 2018 where parts of this work have been discussed and developed.
Version: Accepted for publication
DOI: 10.1016/j.wamoti.2019.02.004
URI: https://dspace.lboro.ac.uk/2134/37164
Publisher Link: https://doi.org/10.1016/j.wamoti.2019.02.004
ISSN: 0165-2125
Appears in Collections:Closed Access (Maths)

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