Nonlinear third harmonic generation in piezoceramics: direct and indirect contributions by intermodulation measurements

The mechanical nonlinearities (NL) of resonant devices can be measured with accuracy by the intermodulation (IM) method to control the behavior of piezoelectric high power devices that work in resonance. The effects of these NL are: increase of losses, shift of the resonant frequency, and frequency hysteresis. The IM of two signals with different amplitudes and frequencies is used to evaluate the direct contribution at frequencies of second and third harmonic signals (first and second overtones), and the indirect contribution at third harmonic. This third harmonic generation is important because it modifies the signal frequency. This work evaluates whether this third harmonic is generated directly by the cubic terms of the high strains in the nonlinear constitutive equations, or indirectly, by the quadratic terms. In fact, these quadratic terms can operate twice on the excitation signal to produce the third harmonic generation. The IM measurement method is used to detect which contribution is more relevant: the direct or the indirect contributions. The results show that in PZT piezoelectric ceramics, with low and high losses, the indirect effect is negligible compared with the direct contribution, since it is about 1000 times lower.