@inproceedings{177529ba57da4262bed45f7a2f533604,
title = "MATHEMATICAL PROOF OF GENERATION OF THE HIGHER HARMONIC AND MODULATED WAVES IN NONLINEAR ELASTIC MEDIUM",
abstract = "It is well known that within the framework of linear elastic theory the action of one wave on another cannot be explained. In this paper we give a general three dimensional theoretical analysis for the interaction between two waves propagating in nonlinear elastic solid. To this end, we use a general Landau-Lifshitz model expanded up to 4th order of nonlinearity for the elastic energy function, which in turn results in the 3rd order of non-linearity in the stress-strain relationship. We show detailed derivations specifically for P- and S-waves with a perpendicular direction of propagation of one wave with respect to another wave. The obtained analytical expressions show that the generation of the higher harmonic and modulated waves is a consequence of a nonlinear relationship between stress and strain in a medium. The obtained theoretical derivations will help to give more insights in understanding of models associated with testing methods such as nonlinear wave modulation spectroscopy and other testing methods.",
keywords = "higher harmonic and modulated waves, nonlinear elastic medium, nonlinear wave modulation spectroscopy, side band generation",
author = "Andrey Melnikov and Christos Spitas",
note = "Publisher Copyright: {\textcopyright} 2024 Proceedings of the International Congress on Sound and Vibration. All rights reserved.; 30th International Congress on Sound and Vibration, ICSV 2024 ; Conference date: 08-07-2024 Through 11-07-2024",
year = "2024",
language = "English",
series = "Proceedings of the International Congress on Sound and Vibration",
publisher = "Society of Acoustics",
editor = "\{van Keulen\}, Wim and Jim Kok",
booktitle = "Proceedings of the 30th International Congress on Sound and Vibration, ICSV 2024",
}