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We investigate nonlinear self-exciting oscillations of elastic plate in transonic flow at unsteady flow conditions: the flow speed is variable in time with different rates. By observing unsteady plate behaviour, we detect bifurcations of limit cycle oscillations. In addition to previously known limit cycle types, new bifurcations of limit cycles are discovered, and their physical nature is revealed. When increasing acceleration of the flow, some of the limit cycles disappear, because they do not have enough time to develop. However, flutter is not fully suppressed even for very high accelerations, though the most destructive higher-mode oscillations are missed.