Peculiarities of formulation and solving the dynamic problems of thermoelasticity

Abstract

The problem of propagation of spherical waves in a thermoelastic medium is considered. Two approaches to taking into account the mutual influence of dynamic fields of deformations and temperature are compared. A generalized model of coupled thermoelasticity is used for calculation in the first approach and the second one is based on the ratio of the theory of thermal stresses, which are neglecting the change of temperature distribution under mechanical loads action. The amplitude-frequency characteristics of radial displacements and normal tangential stresses at the boundary of a spherical cavity being under action of load, which changes according to the harmonic law in time, are obtained. The correspondence between the value of the coupling parameter and the results error caused by the use of the simplified model of field interaction is traced. Wave processes in solids of modern polymeric materials, such as polyvinyl butyral and polyvinyl butyralfurfural belonging to the family of polyvinyl acetals, which have a fairly high coefficient of field connectivity of 0.18 and 0.41, respectively, are considered. It is shown that the use of a simplified model of coupled thermoelasticity for the calculation of structure of such materials leads to unacceptably large differences in the results. Thus, the maximum values of the stress-strained state parameters obtained using the generalized model were 18% higher than in the case of the application of the theory of temperature stresses for polyvinyl butyral. The results difference obtained using this two approaches at some frequencies exceeded 30% for the polyvinyl butyralfurfural medium. It is concluded that the simplified model of the interaction of deformation and temperature fields can be a rough approximation in the analysis of the dynamic reaction of massive structural elements made of such materials.