On the Thermomechanical Analysis and Behavior of Viscoelastic Media Subjected to Cyclic Loading

摘要

The interaction between heating and dynamic response of viscoelastic bodies with temperature-dependent properties is studied. Equations governing the thermomechanical response to sinusoidal loading are developed and shown to be equivalent to a set of two variational principles. Viscoelastic properties of a solid propellant are characterized and then used in numerical examples dealing with sinusoidal shear loading of slabs and cylinders. As the first problem, an approximate variational method is used to calculate one-dimensional transient and steadystate temperature distributions in a massless slab. An exact steady-state solution is obtained for the thermomechanical behavior of a slab with concentrated mass, and is then used to deduce the solution for a similarly loaded cylinder. Finally, the influence of distributed mass in a slab and cylinder is studied using variational principles. It is found that with or without inertia a large temperature rise may occur when the stress is above a certain critical value which depends on thermal and mechanical properties and geometry. Furthermore, the combination of temperature-dependent properties and inertia leads to dynamic jump instabilities that are similar to those existing in a nonlinear spring-mass system. (Author)