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Nonlinear multifrequency model of piezoresonant oscillatory systems

The methodology is proposed of nonlinear multi-frequency model creation of piezoelectric resonators (PR) for an arbitrary number of modes. The equations of the model are reduced to the form of a multi-frequency system with slowly varying amplitudes and fast rotating phases. That permits us to apply the standard methods of analysis. On the basis of the developed model, the equations of multi-current PR characteristics have been obtained for an arbitrary number of interacting modes.