International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

The relevance of the use of various functional elements of piezoelectronics in informational and measuring systems is explained, first of all, by their high reliability, as well as small dimensions and weight, which greatly facilitates the solution of the problem of miniaturization of such systems. Currently, there are no reliable and valid methods of constructing of mathematical models of piezoelectric transducers, which could be used as a theoretical basis for characteristics and parameters calculating of this class of functional elements of modern piezoelectronics. The purpose of this article is to solve the problem of the excitation of transverse bending oscillations in bimorph piezoelectric element. Construction and features of mathematical description of bimorph piezoelectric element, the principle of which is based on the use of axisymmetric transverse bending oscillations, are considered. The solution of the problem of transverse bending oscillations excitation in bimorph piezoelectric element by the difference of electric potentials is obtained.

Thanks to its unique properties piezoceramics has applications in various fields of engineering and technology. Disk piezoelectric devices are widely used in the elements of information systems. Mathematical model of piezoceramic disk transformer with ring electrode in primary electrical circuit is constructed. An estimate is obtained and calculated and experimental curves of the frequency dependence of the modulus of transformation coefficient of piezoceramic disk transformer with ring electrode in primary electrical circuit are compared in the work. As a result of research of real device’s mathematical model a set of geometrical, physical and mechanical and electrical parameters of a real object can be determined which provides realization of technical parameters of piezoelectric functional element specified in technical specifications. The cost of the saved resources is the commercial price of the mathematical model.

A mathematical formulation of the boundary problems of mathematical physics is made, sequential solution which allows describing the stress-strain state and the transfer characteristics of the piezoelectric elements with surfaces partial covering by electrodes. The set of formulated boundary problems makes mathematical content of energy-power method of analysis of the physical condition of the piezoelectric elements in the regime of forced oscillations under the influence of an external source of electrical energy. The proposed sequence of computational procedures can be used in the study of forced oscillations of microelectromechanical structures.