35. Coupled Problem of Thermoviscoelasticity for Composite Polymer Shell of Revolution

The problem of connectedness of mechanical and thermal fields has acquired great practical importance in the mechanics of shells made of polymer composite materials. A number of specific properties of polymers, such as low thermal conductivity, high sensitivity to temperature change, large hysteresis losses, lead to harmonic loading under the effect of heat generation in the body of the shell, namely dissipative heating. To solve the problem of forced vibrations of polymer composite shells, taking into account thermomechanical connectivity, along with effective thermal-viscoelastic characteristics, it is necessary to specify effective thermal characteristics (thermal conductivity, thermal expansion, and specific heat). A complete system of relations is presented, including the equations of forced oscillations of polymer-based composite shells of revolution, heat conduction equations taking into account the effect of heat generation, the constitutive equations of thermoviscoelasticity with the corresponding boundary conditions. As an example, we consider forced axisymmetric vibrations of a fibrous-layered cylindrical shell. In the following, it is assumed that the hard fitting condition is satisfied at the ends of the shell and the temperature is kept constant.