Analysis of acoustic harmonic generation in a solid with multiple nonlinear interfaces

Abstract

Weak bonds and delaminations are typical examples of imperfect interfaces in multilayered structures. Nonlinear acoustic/ultrasonic methods are expected to offer a promising means to monitor these imperfect interfaces, as such interfaces behave nonlinearly when subjected to high-amplitude waves and result in the occurrence of nonlinear frequency components such as higher harmonics. Harmonic generation at a single nonlinear interface has been studied by many investigators from both theoretical and experimental points of view. In this presentation, a theoretical analysis of harmonic generation at multiple nonlinear interfaces is presented within a framework of one-dimensional elastic wave propagation in the frequency domain. The analysis is based on the perturbation expansion of the wave field by assuming the weak nonlinearity. Specifically, the second-harmonic generation is analyzed by first solving the linear transmission of the incident fundamental component, and then the propagation of the second-harmonic components generated at nonlinear interfaces. Some numerical results are demonstrated and compared to the results of time-domain analysis using the finite element method. The present analysis shows that harmonic generation in multilayered solids is remarkably frequency-dependent, as both the fundamental and the harmonic components interact with the layered structure in a complex manner.