Abstract
The measurement of nonlinear parameter of the propagating medium using finite amplitude techniques is based on the detection of the second harmonic generated nonlinearly in the investigated medium. This method requires an analytical expression for the second harmonic. Analytical expressions have been derived for the Gaussian source. For other shapes than Gaussian, a set of Gaussian beams can be used to approximate the pressure distribution at the source. Gaussian coefficients, in the literature, are provided for a uniform source. However, the sources used in many applications radiate non-uniformly because of the manner the piezoelectric element is fixed and because of Lamb waves generated in transducer’s active element. This is of a great importance to derive an analytical expression for the second harmonic for different profile “excitation” of the transducer. Our model is based on the quasilinear theory and a set of Gaussian beams. We used the K-Prony method in order to compute the Gaussian coefficients for each of the uniform, exponential, elliptic and Bessel sources. Using the obtained Gaussian coefficients we showed that the second harmonic magnitude is varying respectively to the used source’s profile. For the measurement of the nonlinear parameter one needs to compute the appropriate values of the Gaussian parameters according to the profile of the used source. One can also use the Gaussian parameters for the uniform source with a correction.
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Jakjoud, H., Chitnalah, A. & Aouzale, N. Transducer profile effect on the second harmonic level. Acoust. Phys. 60, 261–268 (2014). https://doi.org/10.1134/S1063771014030075
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DOI: https://doi.org/10.1134/S1063771014030075