The scientific results on the resonant electromechanical vibrations of piezoceramic plates in the form of disks, rings, and polygons obtained over the last 30 years are analyzed, systematized, and generalized. Emphasis is on experimental methods. It is shown that all piezoceramic plates have vibration modes at which deformations are in-phase over the entire volume of the body Introduction. Thin piezoelectric plates have been a central preoccupation of scientists and engineers for more than one hundred and twenty years passed since the Curie brothers discovered (in 1880) the piezoelectric effect in conductivity experiments on natural crystals. Direct and converse piezoelectric effects are distinguished. The former (piezoelectricity) is that in which mechanical stresses applied to a piezoelectric body induce electric charges on its surface, and the latter (electrostriction) is the deformation of the piezoelectric body caused by charges generated on its surface. The modern piezoelectric transducers employ either direct or converse piezoeffect, or both, as in piezoelectric transformers. In other words, piezoelectric bodies convert electrical into mechanical energy or, vice versa, mechanical into electrical energy. Piezoelectric transformers and transfilters are based on double energy conversion: an electric potential difference is converted into a mechanical stress and then again into a different (higher or lower) electric potential difference. The efficiency of piezoelectric energy conversion is determined by the static and dynamic electromechanical coupling coefficients and the intensity (amplitude) of mechanical vibrations relative to the level of the applied electric power. The piezoelectric effect is a widespread phenomenon observed in many anisotropic crystals, of which quartz, tourmaline, and Rochelle salt have been used since the beginning of the 20th century.A powerful impetus to the development and application of piezoelectricity was the creation, in the 40s of the past century, of synthetic poled piezoceramics based on barium titanate, which was predicted by A. V. Shubnikov even in 1940 [9]. Elements of ultrasonic devices made of poled piezoceramics have a few advantages over natural piezoelectrics such as larger, by an order of magnitude, electromechanical-coupling coefficient. Nowadays, lead-zirconate-titanate solid solutions and their compositions with barium-titanate solid solutions have superseded barium-titanate piezoceramics. But piezoceramics continue to be perfected.In the last decades, piezoelectric, primarily ceramic plates of various geometries have been widely used in vibration detection and control systems, such as actuators and sensors, and in multilayer metal-ceramic structures. Monolithic and composite piezoceramic plates of heterogeneous structure continue to be used in various piezoelectric transformers and frequency filters. Thus, study into the resonant electromechanical vibrations of piezoceramic plates is an important and urgent task of the mechanics of coupled fields in materials an...

An attempt is made to systematize experimental data for a rectangular piezoceramic plate and to compare them with those on planar vibrations of a thin piezoceramic half-disk. Experimental data on planar vibrations of a half-disk are discussed for the first time. Neighboring vibration modes of a rectangular plate with solid electrodes demonstrate strong superposition and coupling Introduction. Rectangular plates made from polarized piezoceramics and natural piezocrystals are of considerable interest in themselves and as models used to study the oscillatory phenomena in elastic structural members. A few results on resonant vibrations of rectangular plates are discussed in [1,3,5,[10][11][12]. The present paper attempts to systematize experimental data on a rectangular piezoceramic plate and to compare them to those on planar vibrations of a thin piezoceramic half-disk. The experimental data addressed here are discussed for the first time. The planar vibrations of piezoceramic plates are such that tensile/compressive strains on the plate surface are accompanied by in-plane shear motions.Measurement of displacement amplitudes during vibrations of a piezoceramic element is still a challenge. This is because of the small size of piezoelectric elements and the low (submicrometer) amplitudes of vibrations. In [4,6], the amplitude of an end of a narrow piezoceramic rectangular fixed at nodal points and undergoing intensive resonant vibrations in the first longitudinal mode was measured with a capacitive probe, followed by the determination of the dynamic stresses at the fixation points and the ultimate strength of the specimen. The efficient method developed by the author many years ago for experimental stress analysis of thin-walled piezoceramic elements made it possible to carry out unique studies of forced resonant vibrations of various piezoelectric specimens. The experimental data obtained with a piezotransformer transducer were reported in many publications reviewed in [13]. The piezotransformer-transducer method allows us to determine, with an uncertainty of 3 to 5%, the sum of the principal mechanical stresses at any point of a thin-walled piezoceramic element under any level of electric or mechanical loading [2,3]. In deriving the relations between the mechanical stresses and the measured potential of the piezotransformer, its area is assumed small and the shape circular.The paper [11] analyzes the effect of the geometry of piezoelectric transformers on their electric potentials and the mutual influence of closely spaced transducers based on experimental data on the resonant radial vibrations of a thin piezoceramic disk with solid electrodes and thickness polarization. The distribution of the sum and difference of the principal mechanical stresses along the radius of this disk can be calculated analytically. It was shown in [11] that the geometry of a piezoelectric transformer has a very weak effect on the distribution pattern of the measured potentials and that the mutual influence of neighboring transducers on ...

The evolution of the planar vibrations of a rectangular piezoceramic plate as its aspect ratio is changed starting with 1 is studied. Experimental data are obtained using an integrated technique based on Meson's circuit, Onoe's circuit, and a piezotransformer transducer. As the aspect ratio increases (square plate becomes rectangular), the intensity of electromagnetic vibrations rapidly increases at the first longitudinal resonance and gradually decreases in the first radial mode. When the aspect ratio is changed so that the length of one of the plate sides remains constant, the resonant frequencies of all vibration modes change too Introduction. Rectangular piezoelectric plates have attracted the attention of scientists and engineers for more than hundred years, beginning with Voigt's pioneering works [25,26]. Over this period, numerous theoretical and experimental publications have been devoted to vibration spectra, electromechanical coupling, and use of plates in resonators and filters. Some of these publications are mentioned in [16]. It is pointed out there that experimental analysis of dynamic stresses in rectangular plates involves so severe difficulties that, for example, Pikalev et al.[3] measured the displacement amplitudes at the ends of a thin, narrow piezoceramic bar and then had to calculate the stresses at its center.Narrow rectangular piezoceramic plates having sections of transverse and longitudinal polarization are used in special devices called piezoelectric transformers which use electromechanical coupling for AC voltage step up/down [4,8,[16][17][18][19]. In the general case where the plate cannot be considered narrow (aspect ratio less than five), the deformation is a very complicated process so that the radial, edge, and even bending resonances appear between the fundamental longitudinal mode L1 and its overtones L3 and L5 [2,16,[22][23][24].The vibrations of a square piezoceramic plate were studied, both analytically and experimentally, in [1], where the resonant frequencies of the first five modes of a 20´20´0.7 mm TsTS-19 plate were calculated and measured in three cases of electric loading corresponding to solid electrodes, diagonal and parallel (along the coordinate axes) grooves in the electrode coating and generating symmetric (about the diagonal) or in-plane bending vibrations. The theoretical and experimental results obtained with solid electrodes practically coincide, whereas the difference between certain frequencies (for example, 101,872 and 91,070 Hz) obtained with grooved electrodes exceeds 11%. This difference between theoretical and experimental data may be attributed to defects in the material and to errors of determining the elastic constants.It should be noted that even the paper [12], in which the vibrations of quartz and tourmaline square plates were studied, points out that longitudinal, (in-plane) bending, radial, and shear modes may exist in such plates. When a square plate undergoes longitudinal vibrations, its expansion along one axis is accompanied by contraction ...

Energy losses in piezoceramic resonators and its influence on vibrations' characteristics This paper is devoted to analyze of the modern achievements in energy loss problem for piezoceramic resonators. In parallel a new simple methodic of an experimental determination of energy losses and coupling coefficients is presented and author's opinion why mechanical quality is different on resonance and anti-resonance is gave. The reason lies in "clamped" capacity and electromechanical coupling factor's value. The better electromechanical coupling the stronger capacity "clamping" and the higher its influence on anti-resonant frequency and quality. Reference 36, figures 4, tables 3.

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