Maths. Physics

Application of wavelet analysis for modeling a nonlinear oscillator

V. V. Narozhnov

Institute of Applied Mathematics and Automation – branch of the FSBSE "Federal Scientific Center "Kabardin-Balkar Scientific Center of the Russian Academy of Sciences", 360000, KBR, Nalchik, Shortanov street, 89 A

Abstract: A simulation model of a nonlinear oscillator in elastic contact with a flat surface was constructed in a graphical environment Simulink. The Cauchy problem describing such an interaction is solved numerically. For the obtained numerical solution, as well as for the sound signals that occur when the probe collides with a solid surface, a wavelet transform is performed. Wavelet analysis of complex acoustic signals allows to detect smallscale features that are necessary for the interpretation of the experiment.

Keywords: mathematical modeling, numerical solution of differential equations, elasticity theory, acoustic signals, wavelet analysis.

UDC: 517.958:531–133

Received: 02.10.2017