Thermal response of a viscoelastic rod under cyclic loading is discussed by determining the stresses and temperature in a viscoelastic rod insulated on its lateral surface and driven by a sinusoidal stress at one end. Temperature dependence of the complex Young’s modulus of the rod and the effect of thermomechanical coupling are included in the analysis. A method of finite differences is used to directly determine the steady-state stresses and temperature without obtaining the complete time history of the process. The iterative algorithm used is very efficient and converges rapidly for a wide range of driving stress amplitudes and frequencies. It is found that rapid rise of temperature to dangerous levels occurs for relatively low values of driving stress amplitudes, especially if the driving frequency is close to one of the critical frequencies of the rod. Drastic softening of the rod leads to large strains. Thus failure of the rod could occur at low values of the driving stress.

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