The resonant radial vibrations of a thin piezoceramic disk with solid electrodes and thickness polarization are considered as an example to study the influence of the geometry of piezotransformer transducers on their electric potentials and the mutual influence of neighboring transducers Keywords: resonant vibrations, piezotransformer transducer, mechanical stresses, electric potentialThe method of piezotransformer transducer [2] turned out to be an efficient tool for experimental investigation of the vibration modes and stress state of thin piezoceramic structural elements. Measuring the displacements of the surface of a piezoceramic element is still a challenge. This is because of both small dimensions of piezoelements and small amplitudes (fractions of a micrometer) of their vibrations. The authors of [1, 12] used a capacitive probe to measure the amplitude of the end of a narrow piezoceramic rectangle fixed at the corners under intensive resonant vibrations in the first longitudinal mode and then calculated the dynamic stresses at the fixation points and the ultimate strength of the specimen. The piezotransformer-transducer method makes it possible to determine, with an uncertainty of no greater than 3-5%, the sum of principal mechanical stresses at any point of a thin piezoceramic element and for any level of electric or mechanical loading [3][4][5]. The governing equations relating the measured potential of the transducer and the mechanical stresses are based on the assumption that it has the form of a disk with small area.In the present paper, we use experimental data on resonant radial vibrations of a thin piezoelectric disk with solid electrodes and thickness polarization to evaluate the influence of the geometry of piezotransformer transducers on their electric potentials and the mutual influence of neighboring transducers. We will perform an exact analysis of the radial distribution of the sum and difference of principal mechanical stresses taking the dielectric, mechanical, and piezoelectric energy losses in piezoceramics into account. The computed and experimental data will be compared.
Relation between Transducer-Measured Potential Difference and Mechanical Stresses.The phenomenological fundamentals of the piezotransformer-transducer (PTT) method are outlined in [2,3,5] and the corresponding amplitude-phase relationships are presented in [4]. During electromechanical resonant vibrations, each electrode transducer (isolated in the main electrode on one of the surfaces of a thin piezoelectric specimen) acquires a charge. The associated potential, measured with a voltmeter, is the complex sum of potential pickup due to capacitive coupling (C r ) with the neighboring electrode coating and the direct piezoelectric potential due to internal mechanical strains.If there were no mechanical vibrations, then the potential of the transducer U c would be defined by the division ratioIf there was no capacitive pickup (C r = 0), then the potential of the transducer would be defined by the piezoelectric charge alon...