О КОЛЕБАНИЯХ ПЬЕЗОКЕРАМИЧЕСКОГО ЦИЛИНДРА С ОКРУЖНОЙ ПОЛЯРИЗАЦИЕЙ

Abstract

The paper deals with of the problem of radial vibrations of a piezoceramic cylinder with circumferential polarization taking into account rheology. The piezoelectric characteristics of the cylinder are functions of the radial coordinate. The cylinder is considered as a piecewise homogeneous electroelastic body consisting of individual prisms. Assuming that the sectioned cylinder is infinitely long and there are no axial deformations in it, boundary value problems on the plane deformation of infinitely long prisms are constructed. In the special case, when all prisms of the sectioned cylinder are in identical conditions of electric loading and external mechanical loads are absent, the boundary problem for the cylinder reduces to the boundary problem for a separate prism. Rheological properties were modeled within the framework of the correspondence principle by replacing the material characteristics with complex moduli-functions of the vibration frequency. A comparison of the concept of complex modules with the widespread linear frequency approximation of the corresponding functions is performed. The solution of the problem was based on the method of shooting. The results of computational experiments on the determination of the amplitude-frequency characteristics for some laws of material inhomogeneity are presented. A series of computational experiments for various inhomogeneity laws and for a different set of initial data is performed, which made it possible to analyze the dependence of the resonant frequencies on the laws of variation of physical characteristics and rheology. A method for reconstructing of the inhomogeneity laws from information on the values of dimensionless functions-radial displacement and radial stress in a certain set of points inside the region using spline approximations is performed. The results of computational experiments have shown sufficient effectiveness of the proposed method.