A nonlinear spring model for an interface between two solids

The solution for second-harmonic fields accompanying an acoustic wave propagating through an interface layer between two solids has been obtained within a second-order perturbation. An approximate boundary model termed as a “nonlinear spring model” has been rigorously developed using an asymptotic expansion of the exact solution in the limit of small ratio of interface layer thickness to wavelength. The applicability of the above model is analyzed by comparison with the exact solution. It is shown that the accuracy of the nonlinear spring model is closely related to some parameters such as the ratio of interface layer thickness to wavelength, and mass densities of layer material to substrates. Parameters that affect the amplitudes of the second harmonics generated at the interface are analyzed by using the nonlinear spring model. ► The nonlinear spring model for an interface is theoretically developed. ► The model uses much fewer parameters. ► Numerical calculations show the applicability of the model. ► Appropriate ‘thickness to wavelength ratio’ can amplify the second harmonic.