Nonlinear reflection of bulk acoustic waves at an interface

Abstract

A theory as the basis for solving nonlinear boundary value problems is described. A new analysis is presented for nonlinear reflection, which reveals that there is a two-dimensional spatial increase of the second-harmonic wave. The accretion along the propagation direction is the result of the self-interaction of the primary wave; the one in the wave front is due to the boundary restriction.

Scattering of time-harmonic elastic waves by an elastic inclusion with quadratic nonlinearity

“…This phenomena has been observed experimentally in solids since the early 1960s (Breazeale and Thompson, 1963;Cantrell et al, 1987), and analytical solutions have been reported in several studies (Lamb, 1925;Keck and Beyer, 1960;Jones and Korbett, 1963;Hikata et al, 1965;Thurston and Shapiro, 1967;Zverev and Kalachev, 1968;Thompson et al, 1976;Thompson and Tiersten, 1977;Sokolov and Sutin, 1983;Cantrell, 1984;Donskoi and Sutin, 1984;Nazarov et al, 1988;Zhou and Shui, 1992;Ostrovsky et al, 2003). A rather comprehensive review of the literature in this subject is given by Cantrell (Cantrell, 2004a).…”

“…The b S given in Eq. (15), however, is associated with the second harmonic shear wave induced by the mode conversion (from the fundamental longitudinal to shear) at an interface (Zhou and Shui, 1992).…”

Contact acoustic nonlinearity in a bonded solid–solid interface

“…It is difficult to give a quantitative value of the bonding strength without destroying the bonding layer. According to some research, the existence of interfaces has prominent influence on the nonlinear propagation of an acoustic wave in solid materials [2][3][4][5][6]. In this paper, we will discuss contact acoustic nonlinearity (CAN) in a bonded solid-solid interface and a CAN model to describe the interface will be proposed.…”

Generation of Cumulative Sum Frequency and Difference Frequency Acoustic Waves in a Two-Dimensional Hard-Walled Waveguide

“…Zhou and Shui [7] have revealed that the e!ect of cumulative growth of re#ected second harmonic, at an interface, arises from both the self-interaction of the primary wave (fundamental wave) and the boundary restriction. For the problem of generation of the cumulative SF and DF waves in the waveguide, the partial waves of the ( f , m) and ( f , n) modes may be considered to be re#ected at the upper and lower walls of the waveguide, i.e., u DK \ and u DL \ , may be considered as the re#ected waves of u DK \ and u DL \ , and vice versa.…”

“…Equation (21) should be satis"ed at any point on the walls of the waveguide, which means that [4,7] [M(…”