Second-harmonic generation in a multilayered structure with nonlinear spring-type interfaces embedded between two semi-infinite media

Abstract

The acoustic second-harmonic generation behavior in a multilayered structure with nonlinear spring-type interlayer interfaces is analyzed theoretically to investigate the frequency dependence of second-harmonic amplitudes in the reflected and transmitted fields when the structure is subjected to the normal incidence of a monochromatic longitudinal wave. The multilayered structure consists of identical linear elastic layers and is embedded between two identical linear elastic semi-infinite media. The layers are bonded to each other by spring-type interfaces possessing identical linear stiffness but different quadratic nonlinear parameters. By combining a perturbation analysis with the transfer-matrix method, analytical expressions are derived for the second-harmonic amplitudes of the reflected and transmitted waves. The second-harmonic amplitudes due to a single nonlinear interface are shown to vary remarkably with the fundamental frequency, reflecting the pass and stop band characteristics of the Bloch wave in the corresponding infinitely extended layered structure. By calculating the spatial distribution of second-harmonic amplitude inside the multilayered structure, the influence of the position of the nonlinear interface as well as the number of layers on the frequency dependence of second-harmonic amplitudes of the reflected and transmitted waves is elucidated. When all interlayer interfaces possess the identical nonlinearity, the second-harmonic amplitudes on both sides of the structure are shown to increase monotonically with the number of layers in the frequency ranges where both fundamental and double frequencies are within the pass bands of Bloch wave. The influence of two non-dimensional parameters, i.e., the relative linear compliance of the interlayer interfaces and the acoustic impedance ratio between the layer and the surrounding semi-infinite medium, on the second-harmonic amplitudes is elucidated.

Second-harmonic generation of two-dimensional elastic wave propagation in an infinite layered structure with nonlinear spring-type interfaces

“…The previous study [37] has shown that the one-dimensional second-harmonic generation in the layering direction of finitely layered structures is closely related to that of infinitely extended layered structures [36], and that the cumulative growth of second harmonics can occur even in the case of a finite number of layers. In light of these results, the findings of the present study are expected to be helpful when analyzing the second-harmonic generation in arbitrary directions of finite layered structures, which is left for the future study.…”

“…For the more general case of multiple interface problem, the authors [35][36][37] have analyzed the second-harmonic generation in multilayered structures with nonlinear spring-type interlayer interfaces by combining a perturbation analysis and the transfer-matrix method [38,39]. As a result, the second-harmonic generation in the presence of multiple imperfect interfaces was found to be influenced by the frequency in a more complicated manner in comparison with the single interface problem, reflecting the band structure of periodic structures.…”

“…As a result, the second-harmonic generation in the presence of multiple imperfect interfaces was found to be influenced by the frequency in a more complicated manner in comparison with the single interface problem, reflecting the band structure of periodic structures. The existing studies on layered structures [32][33][34][35][36][37] are, however, limited to the simplest case of the one-dimensional 3 longitudinal wave propagation in a direction perpendicular to the interfaces. When the interlayer imperfections such as closed delaminations in composite laminates [40][41][42] are characterized using nonlinear acoustic techniques, there are some cases where the normal incidence to the interfaces is unavailable due, for example, to the surrounding environments.…”

Harmonic Generation at a Nonlinear Imperfect Joint of Plates by the S0 Lamb Wave Incidence

“…It was shown in previous studies that when an elastic wave of relatively high amplitude interacts with a contacting interface between solids, nonlinear frequency components such as higher harmonics and sub-harmonics are generated at the interface due to the contact acoustic nonlinearity (CAN) [5][6][7][8][9][10][11][12][13][14]. The nonlinear behavior of elastic waves was reported for not only contacting interfaces but also for adhesive interfaces [15][16][17] and multilayered structures [18,19].…”

“…(19), the interfacial displacement gap by the fundamental wave component [u1 0 ] is obtained, and JAM-19-1334 Mori et al 9 the amplitudes of the reflected and transmitted fundamental waves can be extracted. The amplitude reflection and transmission coefficients of the fundamental extensional wave are expressed as = 1…”