The paper releases results of numerical calculation of axisymmetric dynamic thermoelasticity task for a fixed circular isotropic plate in case of temperature change on its front faces (boundary conditions of the 1st type). The calculated ratios are obtained by using the GL-theory of thermoelasticity (classical theory), which determines the dependence of the vector of heat flux on the velocity of change and temperature gradient. The mathematical model of the task in question includes differential equations of axisymmetric motion and thermal conductivity, formulated as regard to the component of the movement vector and the function of temperature change. Not self-adjoint system is investigated independently. For its solution, a mathematical apparatus technique of separation of variable in the form of finite integral transformations is used, that is transformations of Fourier, Hankel and generalized integral transformation (GIT). The constructed calculation ratios give an opportunity to define stress and strain state and character of distribution of a thermal field of rigidly fixed circular plate with arbitrary axially symmetrical temperature external influence. It is shown, that elastic inertial characteristics of a plate influence the law of change of movement over time only while investigating very thin plates at high-speed temperature impact.

The research focuses on the dynamic axisymmetric task for a round bi-morph structure consisting of a metal support plate and a piezoceramic axially polarized plate. Its bending oscillations are carried out because of the actions of mechanical load (normal stresses) on its end surface, which is an arbitrary time and radial coordinate function. The rigid and hinged support of the plate cylindrical surface is taken into account. The value of the induced field is calculated by determining the potential on the metal support plate. To solve the task of the theory of the elasticity in a three-dimensional model, the authors apply the Hankel finite integral transformations along the axial coordinate and generalized transformation along the radial variable. Besides, at each stage of the study the standardization procedure is carried out. In the first case it is connected with the use of mixed boundary conditions along the radial coordinate to the mixed form, and in the second case heterogeneous boundary conditions are presented as homogenious. The obtained calculation ratios make it possible to determine the optimal thickness of the piezoceramic plate, which allows to make the most effective transformation of the external mechanical effect into an electrical signal. In addition, it is possible to determine changing characteristics of electromagnetic field according to the height of the piezoceramic plate. This principle can be used in the calculation and design of bi-morph systems with graded-varying thickness and rigidity.