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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
W. Nowacki, The Theory of Elasticity [Russian translation], Mir, Moscow (1975).
V. T. Grinchenko, Harmonic Fluctuations and Waves in Elastic Bodies [in Russian], Nauka, Moscow (1981).
I. A. Viktorov, Sound Surface Waves in Solid Bodies [in Russian], Nauka, Moscow (1981).
A. C. Eringen, Microcontinuum Field Theories, Vol. 1: Foundation and Solids, Springer-Verlag, New York (1999).
V. I. Erofeev, Wave Processes in Solids with Microstructure [in Russian], Izd. Mosk. Gos. Univ., Moscow (1999).
A. E. Lyalin, V. A. Pirozhkov, and R. D. Stepanov, “Surface wave propagation in a Cosserat medium, ” Akust. Zh., 28, No. 6, 838–840 (1982).
M. A. Kulesh, V. P. Matveenko, and I. N. Shardakov, “Propagation of elastic surface waves in a Cosserat medium,” Akust. Zh., 52, No. 2, 227–235 (2006).
G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill, New York (1961).
P. Bhatnagar, Nonlinear Waves in One-Dimensional Dispersive Systems, Clarendon Press, Oxford (UK) (1979).
J. D. Achenbach, Wave Propagation in Elastic Solids, North-Holland, Amsterdam-London (1973).
M. A. Kulesh, V. P. Matveenko, and I. N. Shardakov, “Construction and analysis of an analytical solution for the surface Rayleigh wave within the framework of the Cosserat continuum,” J. Appl. Mech. Tech. Phys., 46, No. 4, 556–563 (2005).
Author information
Authors and Affiliations
Additional information
__________
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 http://dx.doi.org/10.1007/s10808-007-0058-z.
Rights and permissions
About this article
Cite this article
Kulseh, M.A., Matveenko, V.P. & Shardakov, I.N. Constructing an analytical solution for lamb waves using the cosserat continuum approach. J Appl Mech Tech Phys 48, 119–125 (2007). https://doi.org/10.1007/s10808-007-0016-9
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10808-007-0016-9