Thermally induced vibration of an internally heated beam

Virtually all previous research on thermally induced vibrations has investigated vibrations caused by surface heating. This paper describes the first detailed study of a thermally induced vibration caused by internal heating. A mathematical model was developed to predict the thermal-structural behavior of an internally heated beam. The results from the model were verified using experimental data for an internally heated beam undergoing thermally induced vibrations. The model was shown to predict the steady-state temperatures accurately. The model predicted the steady-state displacements adequately, although it predicted the displacement histories with some error. The analysis showed that the natural frequency of the beam was more important than the heating rate in determining if vibrations will occur. Once initiated, the amplitude of the vibration increased until the amplitude was such that the heat removed by convection balanced the internal heating. The steady-state amplitude was not affected by the initial displacement of the beam. The convection heat transfer caused the vibrations and controlled the steady-state amplitude. This study showed that thermally induced vibrations of internally heated beams belong to the class of vibrations called self-sustaining oscillations.