Harmonic generation and frequency mixing at nonlinear imperfect interfaces

Abstract

Imperfect interfaces can be found in a variety of natural and artificial systems. Some examples of such interfaces that are objects of ultrasonic evaluation and diagnostics include contacting mechanical components as well as closed defects in structural components. A remarkable feature of these interfaces is that they exhibit highly nonlinear responses to ultrasonic waves. Harmonic generation (generation of, e.g., double frequency signals at the incidence of a wave with a certain frequency) and frequency mixing (generation of sum/difference frequency signals at the incidence of waves of two different frequencies) are typical phenomena at these interfaces. In this presentation, a theoretical analysis of these phenomena is presented based on modeling the interface as a nonlinear spring-type interface between two similar linearly elastic media. Unlike the corresponding nonlinear acoustic effects due to material nonlinearity, the interfacial nonlinear effects considered here do not require the spatial accumulation of nonlinearly generated harmonic or sum/difference frequency components. The propagation directions and amplitudes of these nonlinearly generated components are derived for plane mono- or dichromatic incident waves. Some relevant experimental results for a contacting interface of metallic blocks subjected to different applied pressures are also presented.