Constructing an analytical solution for lamb waves using the cosserat continuum approach |
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Authors: | M A Kulseh V P Matveenko I N Shardakov |
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Institution: | (1) Institute of Mechanics of Continuous Media, Ural Division, Russian Academy of Sciences, Perm’, 614013 |
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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.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 143–150, January–February, 2007.
An erratum to this article is available at . |
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Keywords: | Lamb wave dispersion Cosserat medium analytical solutions |
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