Spectral Energy Dynamics and Wavevector Resonance in a Weakly Nonlinear Chaotic Elastodynamic Billiard

Nonlinear coupling of elastodynamic waves within an elastic body leads to spectral energy redistribution. The coupling strength can exhibit a sharp increase as a function of frequency due to wavevector coincidences between constituent waves of different wave types. The phenomenon is investigated for an ensemble of weakly nonlinear elastodynamic billiards of a generic ray-chaotic shape, with wave fields inside the billiards being treated as fully diffuse and described by a universal statistical theory. A theoretical prediction of the average mode-coupling strength is obtained. Comparison is made between the theory and results of direct numerical simulations performed for an ensemble of two-dimensional rough-wall billiards. The frequency profile of the mode-coupling strength is verified.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Theoretical and Applied Mechanics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Akolzin, Alexey Viktorovich

Contributors dc:contributor

• Weaver, Richard L.

• Physics, Condensed Matter

Language dc:language

eng

Identifier

(MiAaPQ)AAI3250206

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/87737