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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2009, Volume 50, Issue 2, Pages 16–23
(Mi pmtf1712)
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This article is cited in 10 scientific papers (total in 10 papers)
Exact solutions of the equations of motion for an incompressible viscoelastic Maxwell medium
V. V. Pukhnachev Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Abstract:
The unsteady plane-parallel motion of a incompressible viscoelastic Maxwell medium with constant relaxation time is considered. The equations of motion of the medium and the rheological relation admit an extended Galilean group. The class of solutions of this system which are partially invariant with respect to the subgroup of the indicated group generated by translation and Galilean translation along one of the coordinate axes is studied. The system does not have invariant solutions, and the set of partially invariant solutions is very narrow. A method for extending the set of exact solutions is proposed which allows finding solutions with a nontrivial dependence of the stress tensor elements on spatial coordinates. Among the solutions obtained by this method, the solutions describing the deformation of a viscoelastic strip with free boundaries is of special interest from a point of view of physics.
Keywords:
viscoelastic medium, incompressibility, Maxwell relation, Galilean group, partially invariant solution, free boundary motion.
Received: 09.01.2008
Citation:
V. V. Pukhnachev, “Exact solutions of the equations of motion for an incompressible viscoelastic Maxwell medium”, Prikl. Mekh. Tekh. Fiz., 50:2 (2009), 16–23; J. Appl. Mech. Tech. Phys., 50:2 (2009), 181–187
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https://www.mathnet.ru/eng/pmtf1712 https://www.mathnet.ru/eng/pmtf/v50/i2/p16
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Abstract page: | 23 | Full-text PDF : | 17 |
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