The axis-symmetric non-stationary problem of electric elasticity of a piezoceramic cylinder with axial polarization of the material, acting as a converter of energy in the course of the application of the shock-acoustic method of the quality control of concrete structures is considered in the article. The new closed solution represents a consecutive application of methods of finite integral transformations including the Fourier transformation based on the axial coordinate and a generalized algorithm based on the radial variable. Standardization and transformation of boundary conditions into homogeneous ones are performed at each stage. Measurements of electric impulses are taken by a voltmeter that has an electrode coating, and operates as an ideal conductor with negligible mass. The voltmeter is attached to the surface of the cylinder. Simplified electric boundary conditions are used to describe the electric elastic state of the sample under research. More accurate correlations designated to describe the application of a high conductivity voltmeter are considered in this paper to identify the difference of potentials between the electrode planes. Numerous analyses of the research results have proven that the conductivity of the measuring device produces a significant influence on the shape and the maximal intensity of the electric impulse. However, the stress-strained state of the cylinder is changed insignificantly. Besides, dependence of oscillations and shapes of the solid piezoceramic cylinder on electric boundary conditions has been analyzed. The influence of the geometric dimensions of the cylinder on the values of the electric field in the piezoceramic material has been the subject of research.

Рассмотрены нестационарная осесимметричная задача электроупругости для пьезокерамического цилиндра с аксиальной поляризацией материала, который является преобразователем энергии в измерительных приборах ударно-акустического метода контроля качества бетонных конструкций. Новое замкнутое решение построено путем последовательного использования методов конечных интегральных преобразований Фурье по аксиальной координате и обобщенный алгоритм по радиальной переменной.