| Summary: | Under a periodic axial force, a rotating Timoshenko shaft with a rigid unsymmetrical disc was modelled as a parametrically excited system using the finite-element method. Using a harmonic balance method, dynamic stability of the system was checked, steady-state response, undamped resonance condition, and disc centre orbit were solved analytically and discussed numerically. Furthermore, the time history response was calculated to verify the efficiency of the solutions. The discussion shows that the fluctuating part of the axial force results in system dynamic instability, and the parameter regions of dynamic instability are enlarged with increasing amplitude of the fluctuation; the disc centre orbit of the system steady-state response is limited to an annular region, and the orbit width is increased by the axial force fluctuating amplitude; besides the neighbourhood of the system critical speed, the shaft—disc system can undergo some additional resonances due to the fluctuating axial force.
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