Calculation of electrical impedance of disk piezoceramic transformer with a shorted sector electrode in secondary electrical circuit

Piezoelectric disks with partial covering by electrodes of one or two surfaces are often used to create various functional piezoelectronic devices. Disks with sector covering by electrodes are almost the main element of many microelectromechanical systems. Currently, there are no reliable and valid methods of constructing of mathematical models of piezoelectric transformers, which could be used as a theoretical basis for characteristics and parameters calculating of this class of functional elements of modern piezoelectronics. As a result of research of mathematical model of a real device, a set of geometrical, physical, mechanical and electrical parameters of a real object that provides implementation of technical indicators of functional element of piezoelectronics specified in technical task can be determined. This significantly reduces time and cost of the development of new functional elements of piezoelectronics. The cost of the saved resources is the commercial price of mathematical model. The purpose of this article is to determine the difference of electrical potentials according to the scheme of computational procedures of disk piezoceramic transformers with cut electrodes. The main result of this article is that for the first time a theory of non-axisymmetric planar oscillations of a thin piezoceramic disk, which is based on adequate description of physical state of oscillating piezoelectric materials, is constructed