title: Mixing of two co-directional Rayleigh surface waves in a nonlinear elastic material.
abstract: The mixing of two co-directional, initially monochromatic Rayleigh surface waves in an isotropic, homogeneous, and nonlinear elastic solid is investigated using analytical, finite element method, and experimental approaches. The analytical investigations show that while the horizontal velocity component can form a shock wave, the vertical velocity component can form a pulse independent of the specific ratios of the fundamental frequencies and amplitudes that are mixed. This analytical model is then used to simulate the development of the fundamentals, second harmonics, and the sum and difference frequency components over the propagation distance. The analytical model is further extended to include diffraction effects in the parabolic approximation. Finally, the frequency and amplitude ratios of the fundamentals are identified which provide maximum amplitudes of the second harmonics as well as of the sum and difference frequency components, to help guide effective material characterization; this approach should make it possible to measure the acoustic nonlinearity of a solid not only with the second harmonics, but also with the sum and difference frequency components. Results of the analytical investigations are then confirmed using the finite element method and the experimental feasibility of the proposed technique is validated for an aluminum specimen.
authors.affiliation: School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0355.
authors.forename: Merlin B
authors.initials: MB
authors.lastname: Morlock
authors.affiliation: School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0355.
authors.forename: Jin-Yeon
authors.initials: JY
authors.lastname: Kim
authors.affiliation: School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0355.
authors.forename: Laurence J
authors.initials: LJ
authors.lastname: Jacobs
authors.affiliation: Department of Civil and Environmental Engineering, Northwestern University, Evanston, Illinois 60208-3109.
authors.forename: Jianmin
authors.initials: J
authors.lastname: Qu