Dynamic Instability of a Cantilever Column Subjected to a Follower Force Including Thermomechanical Coupling Effect

Within the context of the linear thermoelasticity theory, including thermomechanical coupling effect, the dynamic instability of equilibrium of an elastic cantilever column subjected to a follower-type force at its free end is studied. The surfaces of the column are either kept at constant temperature (isothermal) or thermally insulated (adiabatic). The boundary-value problem is first formulated, and then it is solved in general and in particular for the depth-length ratio much less than unity. Numerical results for the critical loads are given for various values of the thermal parameters. It is shown that, for a tangential follower force, the critical dynamic (oscillatory) instability load may be reduced through the coupling effect to approximately one half of that of the corresponding uncoupled isothermal problem (which was solved by Beck [14] in 1952). Analytical results are also obtained for the damping coefficients for both adiabatic and isothermal boundary conditions. From a comparison with available experiment for aluminum, it appears that material damping, at least for this material, is almost entirely due to thermomechanical coupling.