Abstract
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.
Highlights
When designing building structures and devices of different purpose, there is a need to study them in conditions of uneven non-stationary heating [1,2,3]
Difficulties arising at integrating equations of movement and satisfying boundary conditions, lead to simplification of initial calculation ratios in which inertia forces of elastic system are not taken into account
Another approach is related to the study of the thermal conductivity equation without account of the elastic system deformation [8, 9]
Summary
When designing building structures and devices of different purpose, there is a need to study them in conditions of uneven non-stationary heating [1,2,3] This effect is accompanied with thermal deformations and stresses, which should be taken into account when analyzing strength characteristics of a certain structure. The design scheme of such a construction is presented in the form of thin-walled [4, 5] or infinitely long bodies [6, 7] Another approach is related to the study of the thermal conductivity equation without account of the elastic system deformation [8, 9]
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