TY - GEN
T1 - MATHEMATICAL PROOF OF GENERATION OF THE HIGHER HARMONIC AND MODULATED WAVES IN NONLINEAR ELASTIC MEDIUM
AU - Melnikov, Andrey
AU - Spitas, Christos
N1 - Publisher Copyright:
© 2024 Proceedings of the International Congress on Sound and Vibration. All rights reserved.
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
KW - higher harmonic and modulated waves
KW - nonlinear elastic medium
KW - nonlinear wave modulation spectroscopy
KW - side band generation
UR - http://www.scopus.com/inward/record.url?scp=85205348845&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:85205348845
T3 - Proceedings of the International Congress on Sound and Vibration
BT - Proceedings of the 30th International Congress on Sound and Vibration, ICSV 2024
A2 - van Keulen, Wim
A2 - Kok, Jim
PB - Society of Acoustics
T2 - 30th International Congress on Sound and Vibration, ICSV 2024
Y2 - 8 July 2024 through 11 July 2024
ER -