Open AccessPlane waves in nano-composite materials
Author(s) -
Katerina V. Savelieva,
O. G. Dashko,
Ya. V. Simchuk
Publication year - 2019
Publication title -
vìsnik. serìâ fìziko-matematičnì nauki/vìsnik kiì̈vsʹkogo nacìonalʹnogo unìversitetu ìmenì tarasa ševčenka. serìâ fìziko-matematičnì nauki
Language(s) - English
Resource type - Journals
eISSN - 2218-2055
pISSN - 1812-5409
DOI - 10.17721/1812-5409.2019/1.46
Subject(s) - longitudinal wave , nonlinear system , plane wave , transverse plane , transverse wave , harmonics , harmonic , amplitude , plane (geometry) , physics , mechanics , wave propagation , nanocomposite , classical mechanics , materials science , optics , acoustics , composite material , geometry , structural engineering , mathematics , engineering , quantum mechanics , voltage
The propagation of plane waves in a hyper-elastic medium is theoretically investigated. Two methods of research were used: the method of slowly variable amplitudes and the method of perturbations (successive approximations). The results obtained by these methods are analyzed. The wave interaction in nanocomposite materials is studied. A theoretical study of the cubically nonlinear elastic interaction of plane harmonic waves is carried out for a material whose nonlinear properties are described by the Murnaghan elastic potential. The solution for self-generation of the longitudinal wave is obtained by the method of slowly varying amplitudes. The interaction of transverse horizontally and vertically polarized harmonic waves are studied using the perturbing method. The pumping of energy between different harmonics of a longitudinal wave and various types of transverse waves is described analytically. The results of numerical analysis for various types of nanocomposite materials are presented.