Analysis of Acoustic Second-Harmonic Generation in Alternating Multilayered Structure with Closed Defect at Interlayer Interface

Abstract

The one-dimensional longitudinal wave propagation in the layering direction in an alternating multilayered structure with nonlinear spring-type interfaces is analyzed theoretically to study the second-harmonic generation behavior due to the presence of closed defects at interlayer interfaces. The structure consists of alternating linear elastic layers and is surrounded by two linear elastic semi-infinite media. The layers as well as semi-infinite media are bonded to each other by nonlinear spring-type interfaces possessing identical linear interfacial stiffness and different quadratic nonlinearity to model closed defects such as delaminations and cracks. On the assumption of weak nonlinearity, the second-harmonic amplitudes of the reflected and transmitted waves when a monochromatic longitudinal wave impinges perpendicularly on the structure are derived by combining a perturbation approach with the transfer-matrix method. It is found that the wave propagation characteristics are governed by five non-dimensional parameters: the non-dimensional frequency, the number of interfaces (layers), the acoustic impedance ratio between neighboring media, the stiffness ratio between the interface and the layer, and the ratio of times of flight between neighboring layers. The second-harmonic amplitudes due to a single nonlinear interface are shown to be influenced remarkably by the fundamental frequency as well as the position of nonlinear interface in the multilayered structure. These features are successfully explained by using the pass and stop band characteristics of the layered structure and the spatial distributions of the fundamental and the second-harmonic displacements inside the structure.