Experimental and numerical study of the insert-substitution method: application to the measurement of the nonlinear parameter β of solids

The object of this work is the optimization of the insert-substitution experimental method to determine the nonlinear parameter β of solid plates. The method is based on the comparison of the measured amplitudes of the second order field pressure with and without the sample being immersed in water between the emitter and the receiver. An analytical description of the second order field based on the description of the primary beams as a superposition of Gaussian beams is presented. The model takes into account the sound attenuation and dispersion, and the receiver´s size. The choice of the ultrasonic emitter and receiver (i.e. needle point hydrophone, focused, or non focused transducer) is investigated. Linear and nonlinear ultrasonic waves generated by a focused and a non-focused transducer through a plate are measured. The experimental data is found to be in good agreement with the model predictions