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

摘要

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