Theoretical Development of Nonlinear Spring Models for the Second Harmonics on an Interface between Two Solids

Based on the exact solutions for the second-harmonic generations of the fundamental longitudinal and transverse waves propagating normally through a thin elastic layer between two solids, the approximate representations termed as `nonlinear spring models' relating the stresses and displacements on both sides of the interface are rigorously developed by asymptotic expansions of the wave fields for an elastic layer in the limit of small thickness to wavelength ratio. The applicability for the so-called nonlinear spring models is numerically analyzed by comparison with exact solutions for the second harmonic wave reflections. The present nonlinear spring models lay a theoretical foundation to evaluate the interfacial properties by nonlinear acoustic waves.