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The study of the fluid-interaction phenomena of a spinning disc bounded in compressible fluid filled environment is an important engineering problem in the aspect of the design concern that has important relevance in modelling the real life industrial problems such as computer hard drives and turbine rotor dynamics. In a damped system with a constant spin rate, the interaction between the transverse oscillations of disc with the acoustic oscillations of the surrounding fluid leads to a aeroelastic travelling flutter instability by through a Hopf bifurcation [1]. However, due to fluctuations in the disc spin rate, there can be either a change in the existing instability mechanism or a possibility of new instabilities. Hence, it is important to know all the possible instability mechanisms in the present fluid structure interaction system by considering the effects of the perturbation in the disc spin rate. By assuming a harmonic perturbation in the disc spin rate, the bifurcation analysis presented in [1] has been extended to the perturbed system. The field equations governing the disc oscillations and the acoustic oscillations are coupled by means of the interface boundary conditions and are discretized as in [1]. The resulting equations form a non-autonomous non-conservative gyroscopic system. Using these equations, a series of bifurcation analysis have been performed by considering the mean speed, the amplitude and frequency of the harmonic perturbation as bifurcation parameters. The study shows that the coupled system undergoing a pitchfork bifurcation where the bifurcation parameter is the amplitude of the harmonic perturbation. During this bifurcation, the plane equilibrium becomes unstable and a new equilibrium solution emerges. The resulting time histories in terms of a particular disc mode for two different amplitudes are given Fig. 1. As in Fig. 1(a), for a = 0.15, the oscillations of the particular mode is exhibiting a decaying response. Whereas, for a = 0.9, the system exhibits a quasi periodic response as in Fig. 1(b). Further discussions about these responses and the results for other cases (mean speed and the frequency of the harmonic perturbation) could not be discussed here for the sake of brevity and will be included in the full length paper.