МАТЕМАТИЧНИЙ ОПИС БІМОРФНОГО П'ЄЗОЕЛЕКТРИЧНОГО ЕЛЕМЕНТА

Abstract

The relevance of the use of various functional elements of piezoelectronics in power and informational 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. The technologies and devices that use the direct and / or reverse piezoelectric effect in the principles of their work are promising. The purpose of this article is to solve the problem of the excitation of transverse bending oscillations in bimorph piezoelectric element. With the help of a personal computer, it is possible to work out several combinations of geometrical, physical and mechanical parameters of a specific design of piezoelectric transformer within a few hours, and to find a combination of them that ensures the implementation of the specified parameters of the device. Manipulating geometrical parameters of electrodes and their location relative to each other, one can have a significant effect on the energy of oscillatory motion particular type of material particles of piezoelectric disk volume. This allows to reduce the number of experiments that are inevitably performed in the process of developing new devices. In addition, using a mathematical model, the sensitivity of piezoelectric transformer characteristics to variations in the parameters of its design elements is easily determined. Having these dependencies, it is possible to make a rational choice of the technology for manufacturing a product, that is, to choose from a number of technologies the least expensive one. Thus, a qualitative mathematical model can significantly reduce the time and cost of developing new models of piezoelectric transformers. The main result of this article can be fixed as follows: the construction and features of mathematical description of bimorph piezoelectric element, the operating 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.