Simple and Sawtooth Waves in a Resonance Layer with Quadratic Elastic Nonlinearity

Abstract

We study the excitation of simple and sawtooth discontinuous waves in a nonlinear acoustic resonator representing a plane-parallel layer located in an outer medium and irradiated by a normally incident plane-longitudinal harmonic wave. The amplitudes of the wave at the fundamental frequency and its harmonics, which are emitted by the layer to the outer medium, are determined. Expressions are obtained for the linear and nonlinear Q-factors of such a resonator. The way to determine the nonlinearity parameter of the medium in the layer is discussed on the basis of measuring the amplitude of the second harmonic emitted by the layer to the outer medium in the forward and backward directions relative to the incident wave.