The problem of longitudinal oscillation of a viscoelastic rod of finite length including the effect of thermomechanical coupling has been studied. The material is assumed to be thermorheologically simple. The almost steady oscillation superposed on a slowly varying temperature distribution permits representation as a boundary-value problem which is solved numerically by iterative procedures. Calculations are made for different stress levels and frequencies. It is found that the temperature increases considerably after a length of time of vibration although the stress level is low. A steady state of temperature can be reached if the temperature at one end of the rod is fixed and a radiation boundary condition is prescribed at the other end.

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