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Some Invariant Solutions of Two-Dimensional Elastodynamics in Linear Homogeneous Isotropic Materials

Published online by Cambridge University Press:  03 June 2015

Houguo Li  and
Kefu Huang
Houguo Li*
Affiliation:
Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China
Kefu Huang*
Affiliation:
Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China
*
Email: awawdeh@hu.edu.jo
Corresponding author. Email: abbasbandy@yahoo.com
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Abstract

Invariant solutions of two-dimensional elastodynamics in linear homogeneous isotropic materials are considered via the group theoretical method. The second order partial differential equations of elastodynamics are reduced to ordinary differential equations under the infinitesimal operators. Three invariant solutions are constructed. Their graphical figures are presented and physical meanings are elucidated in some cases.

Keywords

74B0535Q7422E70Elastodynamicsgroup theoretical methodinvariant solution
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Issue 2 , April 2013 , pp. 212 - 221
Copyright
Copyright © Global-Science Press 2013

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References

[1]Kausel, E., Fundamental Solutions in Elastodynamics: A Compendium, Cambridge: Cambridge University Press, 2006.Google Scholar
[2]Kachanov, M., Shafiro, L. and Tsukrov, I., Handbook of Elasticity Solutions, Dordrecht/Boston/London: Kluwer Academic Publishers, 2003.Google Scholar
[3]Chand, R., Davy, D. T. and Ames, W. F., On the similarity solutions of wave propagation for a general class of non-linear dissipative materials, Int. J. Nonlinear Mech., 11(3) (1976), pp. 191– 205.CrossRefGoogle Scholar
[4]Ames, W. F. and Suliciu, I., Some exact solutions for wave propagation in viscoelastic, viscoplastic and electrical transmission lines, Int. J. Nonlinear Mech., 17(4) (1982), pp. 223–230.CrossRefGoogle Scholar
[5]Ames, K. A., Group properties of a one-dimensional system of equations for wave propagation in various media, Int. J. Nonlinear Mech., 24(1) (1989), pp. 29–39.CrossRefGoogle Scholar
[6]Bokhari, A. H., Kara, A. H. and Zaman, F. D., Exact solutions of some general nonlinear wave equations in elasticity, Nonlinear Dyn., 48(1-2) (2007), pp. 49–54.CrossRefGoogle Scholar
[7]Ovsiannikov, L. V., Group Analysis of Differential Equations (translated by Chapovsky, Y., Translation edited by Ames, William F.), New York: Academic Press, 1980.Google Scholar
[8]Chandrasekharaiah, D. S., Naghdi-Hsu type solution in elastodynamics, Acta Mech., 76(3-4) (1989), pp. 235–241.CrossRefGoogle Scholar