A system of nonlinear measurement and nonlinear elastic characterization of resonators is presented, which increases the possibilities and characteristics of the other classic nonlinear characterization methods. This characterization has been necessary due to the use of resonators in power devices, where their behavior departs from the linear characteristics. The use of burst signals and a system of acquisition and data processing is proposed instead of impedance analyzers, thus avoiding the thermal effects associated with the high-signal measures, which are necessary for this characterization. The measures are repeated for different amplitudes and at the same frequency near the resonance by a single amplitude sweep, which is simpler and faster to carry out than the multiple frequency sweepings used in other methods. As a last resort, a variation on the proposed method, closer to the classical measures, is put forward, in which the resonance is ensured in all the measures. Special emphasis is placed on obtaining nonlinear characterization of the piezoceramic material in order to increase its optimization in the transducers in terms of both its use and its composition and structure.

We experimentally demonstrate the effective rocking of a nonlinear electronic circuit operating in a periodic regime. Namely, we show that driving a Chua circuit with a periodic signal, whose phase alternates (also periodically) in time, we lock the oscillation frequency of the circuit to that of the driving signal, and its phase to one of two possible values shifted by π, and lying between the alternating phases of the input signal. In this way, we show that a rocked nonlinear oscillator displays phase bistability. We interpret the experimental results via a theoretical analysis of rocking on a simple oscillator model, based on a normal form description (complex Landau equation) of the rocked Hopf bifurcation.

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La aplicación de campos eléctricos o esfuerzos mecánicos elevados sobre piezocerámicas PZT produce una alteración de los coeficientes elásticos y dieléctricos, así como de sus pérdidas. En este trabajo se establece un procedimiento que permite la comparación entre el comportamiento no lineal dieléctrico de una cerámica con el comportamiento no lineal elástico medido en el primer modo de oscilación radial, describiéndolos mediante magnitudes adecuadas. Se observa un comportamiento cualitativamente distinto entre los materiales PZT blandos y duros. Para un mismo material, los comportamientos dieléctrico y mecánico son claramente semejantes, así como las pérdidas de uno y otro tipo. Esto se puede interpretar si se asume que la no linealidad se produce gracias a la interacción de las paredes de dominio con los defectos, y si solo intervienen apreciablemente las paredes de no-180º. Se analizan diversos factores a tener en cuenta en esta comparación, como son el tipo de no linealidad, la distribución de las orientaciones de los dominios, o la falta de uniformidad del campo. Ello puede permitir relacionar el comportamiento no lineal con la función de distribución (que define el estado de la cerámica) o la interpretación del comportamiento de los modos superiores.Palabras clave : piezoeléctrico, cerámica, no linealidad, dieléctrico, elasticidad. Relation between dielectric and mechanical nonlinear behaviours in PZT piezoelectric ceramics.Elastic and dielectric coefficients of PZT piezoceramics are perturbed by applying high electric field or high mechanical stress. In this work, a procedure is described in order to compare non-linear dielectric and elastic behaviour, by using suitable quantities. Qualitative differences are observed between soft and hard materials. But, for a given material, dielectric and mechanic behaviours are very similar, as well as the losses of both kinds. This fact can be understood by assuming that non-linearity is produced by interaction between domain walls and defects, and that 180º walls are negligible in front of non-180º walls. Some facts must be taken into account in order to compare both behaviours, as the non-linear model, the domain wall orientation distribution, or the non uniformity of the fields. This allows to relate the non linear behaviour with the distribution function, that defines the material state, or to understand the non-linearity produced at the overtones.Key words: piezoelectric, ceramics, non-linearity, dielectrics, elasticity. INTRODUCCIÓNLas cerámicas piezoeléctricas se han hecho insustituibles en muchos dispositivos de potencia en los que se requiere un buen factor de acoplo electromecánico, pero cuando se requieren además máximas prestaciones hay que usar dichas cerámicas en condiciones límite. Desafortunadamente, su comportamiento en estas condiciones es altamente no lineal, siendo sus características fuertemente dependientes del campo aplicado. Por ello, es necesario no solo descubrir el origen interno de dicho comportamiento, lo que nos permitiría posiblement...

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