Related thermoelastic elastomeric task for long cylinder.

A new closed solution of the coupled non-stationary problem of thermoelectroelasticity for a long piezoceramic radially polarized cylinder is constructed when the boundary conditions of the 1st kind of thermal conductivity are satisfied on its front surfaces. The case is considered when the rate of change of the temperature field does not affect the inertial characteristics of the elastic system, which makes it possible to include in the initial calculated relations of the problem under consideration the linear equations of equilibrium, electrostatics and thermal conductivity with respect to the radial component of the displacement vector, electric potential, as well as the function of changing the temperature field. The calculations use the classical Fourier law of thermal conductivity. To solve the problem, the mathematical apparatus of incomplete separation of variables is used in the form of a generalized biorthogonal finite integral transformation (CIF), based on a multicomponent relation of eigenvector-functions of two homogeneous boundary value problems. An important point in the procedure of the structural algorithm of this method is the selection of the adjoint operator, without which it is impossible to solve non-self-adjoint linear problems of mathematical physics. [ABSTRACT FROM AUTHOR]