Key Features of the Transient Amplification of Mistuned Systems

The dynamic behavior of bladed disks in resonance crossing has been intensively investigated in the community of turbomachinery, addressing the attention to (1) the transient-type response that appear when the resonance is crossed with a finite sweep rate and (2) the localization of the vibration in the disk due to the blade mistuning. In real conditions, the two mentioned effects coexist and can interact in a complex manner. This paper investigates the problem by means of analytic solutions obtained through asymptotic expansions, as well as numerical simulations. The mechanical system is assumed as simple as possible: a 2DOF linear system defined through the three parameters: damping ratio ξ, frequency mistuning Δ, rotor acceleration $Ω̇$⁠. The analytic solutions are calculated through the multiple-scale method.