Second Harmonic Generation Through a Plate Immersed in Water: Theory and Experiment

In linear acoustics, the pressure field transmitted through a plate immersed in water is commonly used to determine the characteristics of the object. The aim of this work is to extend the approach to the quasi-linear case. The so-called insertion/substitution method consists in comparing the amplitude of the transmitted field with and without the sample whose parameters are to evaluate. An initially sinusoidal plane wave normally incident upon the plate is considered. The second order pressure field is described analytically, based on the solution to the Westervelt equation, from series of reflected and transmitted waves at the interfaces. Attenuation, dispersion and diffraction effects for the fundamental component are included in the model. Firstly, it is shown that the derived expression can be separated into three components according that harmonic generation occurs before, in or beyond the plate. Secondly, the source terms for harmonic generation are identified. Furthermore, experimental data obtained from aluminum plates are compared to results from the analytical expressions. The ability to deduce the nonlinear coefficient of a solid plate from such an experimental configuration is discussed.