Two-dimensional wave propagation in an elastic half-space with quadratic nonlinearity: A numerical study

Sebastian Küchler, Thomas Meurer, Laurence J. Jacobs, Jianmin Qu

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Abstract

This study investigates two-dimensional wave propagation in an elastic half-space with quadratic nonlinearity. The problem is formulated as a hyperbolic system of conservation laws, which is solved numerically using a semi-discrete central scheme. These numerical results are then analyzed in the frequency domain to interpret the nonlinear effects, specifically the excitation of higher-order harmonics. To quantify and compare the nonlinearity of different materials, a new parameter is introduced, which is similar to the acoustic nonlinearity parameter β for one-dimensional longitudinal waves. By using this new parameter, it is found that the nonlinear effects of a material depend on the point of observation in the half-space, both the angle and the distance to the excitation source. Furthermore it is illustrated that the third-order elastic constants have a linear effect on the acoustic nonlinearity of a material.

Original languageEnglish
Pages (from-to)1293-1301
Number of pages9
JournalJournal of the Acoustical Society of America
Volume125
Issue number3
DOIs
StatePublished - 2009

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