Thermally induced vibrations due to internal heat generation

Virtually all previous research on thermally induced vibrations has investigated vibrations caused by surface heating. This is the first detailed study of a thermally induced vibration caused by surface cooling. The phenomenon is shown to be driven by thermal moments. The thermal moments are caused by convection because the vibrations occur in air but not in a vacuum. A mathematical model was developed to predict the thermal-structural behavior of an internally heated beam. The convection heat transfer for a vibrating beam is complex. In most cases it is neither completely natural nor completely forced convection. The convection heat transfer is a mix of both components. The convection is further complicated by the transition of the airflow along the beam from laminar to turbulent flow. An experimental heat transfer investigation was conducted to determine expressions for the natural and forced convection as functions of both position along the beam and velocity. 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 adequately predicted the steady-state displacements, although it predicted the displacement histories with some error. The analysis showed that the thermal and structural problems are coupled by the forced convection. Once initiated, the amplitude of the vibration increases until the amplitude is such that the heat removed by convection balances the internal heating. The steady-state amplitude is not affected by the initial displacement of the beam. Thermally induced vibrations of internally heated beams belong to the class of vibrations called self-sustaining oscillations.