Thermal instability of a layered viscoelastic rectangular prism under high-frequency shear loading

Within the framework of a coupled problem of thermoviscoelasticity, using the method of numerical modeling, we have studied the thermal instability of a rectangular prism, composed of copper and polyethylene or polymethylmethacrylate layers, in the course of its dissipative heating. The prism is subjected to high-frequency force or kinematic shear. We have established that, in the case of polyethylene, thermal instability occurs under conditions of force loading and is absent under a kinematic one. However, for polymethylmethacrylate, thermal instability takes place for both cases of loading. This effect is attributable to the existence of temperature intervals where the shear and volume loss compliances for each of the polymers increases with the temperature. We have also revealed that the critical values of thermal instability for a prism with metal layers are substantially higher than those for a homogeneous prism. In addition to thermal instability, thermal resonance instability is also possible. It is caused by the jump of the thermal state from the low- to high-temperature branch of the soft-type resonance characteristic. UDC 539.3
Vibratory heating induced by intense vibrations of viscoelastic solids can lead to a substantial growth of their temperature (8, 11, 14). Upon reaching the temperature of softening or melting of [...]