A physical device for the measurement of weak harmonic distortions radiated from a piezoelectric rod

In the field of Non-Destructive Evaluation (NDE), Third Order Constants (TOC) of a material can be evaluated using the acoustic harmonic generation method, based on the spectral modification of an acoustic wave within a sample under test. Regarding freely resonating piezoelectric rods, electromechanical and elastic TOC values have been reported [1]. However, the authors highlight the difficulty to obtain accurate measurements of weak classical non-linear effects as, in solids, they can be very low compared to linear phenomena. The purpose of this study is to design, build and test a physical device that promotes non-linearity from a piezoelectric element in order to improve the accuracy of non-linear measurements.  By analogy to signal conditioning stages in analog electronics, the proposed acoustic device performs both amplification and filtering. First, the system is designed so that some eigenmodes can amplify the non-linear component originating from the piezoelectric rod. In a second step, the amplified component is transmitted through a periodic medium that filters the primary wave. Thus, the  amplitude ratio  between harmonic (h 2 ) and fundamental (h 1 ) components is enhanced at the output of the system.  The experimental device is composed of the piezoelectric rod, and alternating rods of aluminum and steel. The needed geometrical characteristics were obtained using a one-dimensional functional model of wave propagation in the case of quadratic non-linearity. It enables the modeling of elastic and piezoelectric media in the form of equivalent electrical circuits based on the hexapole formalism and extended to the non-linear case [2]. The non-linear constants of the piezoelectric element (input data in the model) were previously measured [1]. The displacement field is measured at the output of the system. Several frequencies for h 1 (in the stop band of the filter, around 30 kHz) were tested experimentally. In each case, the behaviour of the system was correctly predicted by the theory. The model shows that the measured output non-linear field is only originating from the piezoelectric material. With the proposed system, the ratio h 2 /(h 1 2 ) of the displacement field was increased by a factor comprised between 10 3 and 10 5 approximately, depending of the chosen frequency. Furthermore, the amplitude of the harmonic displacement is maintained at around 3 nm, which makes the measurement quite accurate. [1] IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 56 (1), 167-174 (2009). [2] Ultrasonics 51 (2), 109-114 (2011).