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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2007, Volume 48, Issue 1, Pages 143–150
(Mi pmtf2003)
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This article is cited in 6 scientific papers (total in 6 papers)
Constructing an analytical solution for Lamb waves using the Cosserat continuum approach
M. A. Kulesh, V. P. Matveenko, I. N. Shardakov Institute of Mechanics of Continuous Media, Ural Division, Russian Academy of Sciences, Perm’, 614013
Abstract:
The problem of propagation of a Lamb elastic wave in a thin plate is considered using the Cosserat continuum model. The deformed state is characterized by independent displacement and rotation vectors. Solutions of the equations of motion are sought in the form of wave packets specified by a Fourier spectrum of an arbitrary shape for three components of the displacement vector and three components of the rotation vector which depend on time, depth, and the longitudinal coordinate. The initial system of equations is split into two systems, one of which describes a Lamb wave and the second corresponds to a transverse wave whose amplitude depends on depth. Analytical solutions in displacements are obtained for the waves of both types. Unlike the solution for Lamb waves, the solution obtained for the transverse wave has no analogs in classical elasticity theory. The solution for the transverse wave is compared with the solution for the Lamb wave.
Keywords:
Lamb wave, dispersion, Cosserat medium, analytical solutions.
Received: 30.03.2006
Citation:
M. A. Kulesh, V. P. Matveenko, I. N. Shardakov, “Constructing an analytical solution for Lamb waves using the Cosserat continuum approach”, Prikl. Mekh. Tekh. Fiz., 48:1 (2007), 143–150; J. Appl. Mech. Tech. Phys., 48:1 (2007), 119–125
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https://www.mathnet.ru/eng/pmtf2003 https://www.mathnet.ru/eng/pmtf/v48/i1/p143
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