Effect of cyclic loading on the temperature in viscoelastic media with variable properties

Steady-state and transient temperature distributions resulting from dissipation are calculated for a linear viscoelastic slab and hollow cylinder subjected to cyclic shear loading Temperature dependence of the dissipation function is introduced through the familiar assumption of thermorheologically simple behavior, wherein frequency-dependent mechanical properties measured at different temperatures are superposed by shifting with respect to the logarithmic frequency scale This assumption leads to a nonlinear heat-conduction equation, and an exact closed-form solution is obtained for just the steady-state temperature distribution In order to solve the transient problem, two approximate methods of analysis are proposed Numerical results for a solid propellant are given, and it is found that a large temperature rise will occur as the result of a thermal instability when the shear stress is above a certain critical value that depends on thermal and mechanical properties and geometry In this paper, inertia is neglected; however, many of the considerations, including the approximate methods, are potentially applicable to dynamic problems as well as to other configurations and loading conditions