Green-function Method for Nonlinear Interactions of Elastic Waves

Abstract

In the linear wave propagation regime, an analytical mesh-free Green-function decomposition has been shown as a viable alternative to FDTD and FEM. However, its expansion into nonlinear regimes has remained elusive due to the inherent linear properties of the Green-function approach. This work presents a novel frequency-domain Green function method to describe and model nonlinear wave interactions in isotropic hyperelastic media. As an example of the capabilities of the method, we detail the generation of sum frequency waves when initial quasimonochromatic waves are emitted in a fluid by finite sources. The method is supported by both numerical and experimental results using immersion ultrasonic techniques.

An iterative method to evaluate one-dimensional pulsed nonlinear elastic wavefields and mixing of elastic waves in solids

“…As a consequence, all of these orders must be stored, and the physical interpretation of the scheme is complex. Demc ˇenko et al 20 provide a general Green's function representation for the nonlinear interaction of elastic waves and apply this to compute the interaction of a propagating shear wave and an evanescent compressional wave at a fluid-solid interface. Mazilu et al 21 present a plane wave method to describe the nonlinear interaction of beams with finite widths and pay explicit attention to incident evanescent waves, for which classical momentum conservation does not apply.…”