caa a22 4500 606166904 CHVBK 20210128100700.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10665-014-9723-4 doi (NATIONALLICENCE)springer-10.1007/s10665-014-9723-4 Domański Włodzimierz Military University of Technology, Faculty of Cybernetics, Institute of Mathematics and Cryptology, Gen. S. Kaliskiego 2, 00-908, Warsaw 49, Poland aut The complex Burgers equation as a model for collinear interactions of weakly nonlinear shear plane waves in anisotropic elastic materials [Elektronische Daten] [Włodzimierz Domański] Collinear interactions of weakly nonlinear quasi-shear plane waves in anisotropic (in particular fiber-reinforced) compressible elastic materials are analyzed. Evolution equations for quasi-shear wave amplitudes are derived with the help of the asymptotic method of a double-scale expansion. It is shown that quadratically nonlinear coupling is possible when shear waves propagate along a special fiber direction in anisotropic materials. The evolution equations are reduced to a single inviscid complex Burgers equation when the fiber direction is a threefold symmetry acoustic axis. Some properties of this equation are analyzed. General considerations are illustrated on examples of shear waves propagating along a threefold symmetry acoustic axis in a cubic crystal and in an icosahedral quasicrystal. The Author(s), 2014 Anisotropic elastic materials nationallicence Complex Burgers equation nationallicence Cubic crystal nationallicence Icosahedral quasicrystal nationallicence Quadratically nonlinear coupling nationallicence Shear waves nationallicence Threefold symmetry acoustic axis nationallicence Journal of Engineering Mathematics Springer Netherlands 95/1(2015-12-01), 267-278 0022-0833 95:1<267 2015 95 10665 https://doi.org/10.1007/s10665-014-9723-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10665-014-9723-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Domański Włodzimierz Military University of Technology, Faculty of Cybernetics, Institute of Mathematics and Cryptology, Gen. S. Kaliskiego 2, 00-908, Warsaw 49, Poland aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Springer Netherlands 95/1(2015-12-01), 267-278 0022-0833 95:1<267 2015 95 10665