Nonaxisymmetric dynamic problem of the direct piezoeffect for axially polarized solid cylinder

The paper considers nonaxisymmetric dynamic problem for the theory of electroelasticity of anisotropic piezoceramic cylinder axially polarized. Mechanical vibrations are carried out by the action of its end surfaces of the non-stationary load as normal stresses; it is an arbitrary function of the radial, angular position and time. At the same end the surfaces are covered with electrodes and fixed membranes. The developed algorithm of calculation allows to meet a variety of mechanical and electrical conditions on the cylindrical surfaces of the electrodes that are not covered. To be specific, in this paper, they are considered free from normal and shear stresses. The new closed solution is built in three-dimensional statement through the consistent use of the method of incomplete separation of variables in the form of integral transformations. The author has consistently applied Fourier transformation with finite limits on the axial coordinate and the final transformation of generalized (FIT) for the radial variable. At each stage of the decision-making, the standardization is utilized that allows one to bring the boundary conditions on the corresponding coordinate in uniform. The calculated ratio the components of the displacement vector and the electric field potential make it possible to determine the frequency of natural oscillations nonaxisymmetric, stress-strain state of the piezoceramic cylinder, and all parameters induced by the electric field. The potential difference between the end faces is determined by a measuring instrument with a high input impedance which corresponds to the “idle”. The numerical results of calculation lead to the conclusion that the use of the constructed algorithm makes it possible, compared with the numerical methods, to obtain more accurate values of natural frequencies of the spectrum, the stress-strain state and the electric field of the piezoceramic cylinder.