Yurchenko M. Eduction of henerogeneity of elastic properties of thin-walled elementі by the change of resonsnce frequency longitudinal and flexural natural vibrations (method of low-frequency tomography).

Dissertation thesis is concerned with eduction of heterogeneity of elastic properties of construction elements by so called method of low-frequency tomography. Generalizing the results of preconceptual study the author gives mathematical basics of the considered method in the accomplished form. The author represents full (not diagonal) set of eguations for the coefficients of truncated Fourier series to which target heterogeneity is approximating. This result is concequece of thorough analysis of primal problems and introduction of allied to normal modes of vibrations of full orthogonal systems of functions. Adequancy of results was verified by experimental research of longitudinal vibrations of piezoelectric ceramic rod with heterogeneity. Which appears as a result of separation by dielectric gap of the part of electrode coating from operating electrodes. In the experiment the author managed to measure with high degree of accuracy the first six frequencies of natural vibrations for piezo rod as well as for the sample with separated electrodes. The plots of defect renovation are enclosed. Key words: heterogeneity of elastic properties, inverse problems of vibrations, low - frequency tomography, piezoelectric ceramic materials.