Yanchevskyi I. Direct and inverse problems of nonstationary deforming of bimorph electroelastic elements of constructions

The thesis deals with the development of effective numerically-analytical approaches for investigation of transient operating modes for bimorph electroelastic elements of constructions (made of rigidly connected polarized by thickness piezoceramic and piezoelectrically passive elastic layers) under the impulse electromechanical loading, as well as with carrying out calculations for specific piezotransducers, analyzing the results and revealing regularities of their nonstationary deformation. On the basis of these approaches and using methods of theories of ill-posed problems of calculus mathematics and those of optimal control, the methods for solving boundary "inverse" problems in identification of nonstationary electromechanical loadings acting on piezotransducers have been developed. The research has been conducted for the elements in the form of thin-walled beams, rectangular and round plates, cylindrical and spherical shells, including nonclosed ones, as well as hollow cylinders and spheres. In case of thin-walled bimorph piezotransducers the problem is set within the limits of the linear theory based on the Kirchhoff-Love's hypotheses generalized for electromechanics. To research transient processes in hydroelectroelastic systems of a hollow bimorph cylinder or a sphere submerged in an ideal compressible liquid and connected to the generator of non-stationary electric voltage through an electric circuit with the consequently connected concentrated parameters, the relations of linear electroelasticity, an acoustic approach and Kirchhoff's law for electric circuit have been used. In case of piezotransducers with the complex geometry for which realization of analytical methods for solving "direct" problems is attended with principle mathematical difficulties, regularities of their nonstationary deformation have been investigated with the help of the bundled software that realizes the finite elements method. The approaches suggested in the work can be used as a theoretical and practical basis for engineering calculations and solving optimization problems for bimorph piezotransducers which work under impulse electromechanical loads.