Spectral Energy Dynamics and Wavevector Resonance in a Weakly Nonlinear Chaotic Elastodynamic Billiard
Akolzin, Alexey Viktorovich
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https://hdl.handle.net/2142/87737
Description
Title
Spectral Energy Dynamics and Wavevector Resonance in a Weakly Nonlinear Chaotic Elastodynamic Billiard
Author(s)
Akolzin, Alexey Viktorovich
Issue Date
2006
Doctoral Committee Chair(s)
Weaver, Richard L.
Department of Study
Theoretical and Applied Mechanics
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Condensed Matter
Language
eng
Abstract
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.
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