As an initial step toward understanding the fully coupled dynamics of mistuned bladed disk-shaft systems, this paper investigates the frequency characteristics of natural whirl speeds associated with the in-plain vibration of a rotating mistuned bladed disk mounted on an isotropic support. Through complex multi-blade coordinate transformation and modulation, a simplistic analysis model describing the essential in-plain whirling behavior of mistuned bladed rotor is derived in a typical form of linear differential equations with time-constant coefficients. By applying ordinary eigenvalue analysis for linear time-invariant systems, the whirl speeds of mistuned bladed rotor are examined for cases of weak and strong inter-blade coupling conditions. The mistuning effect on the whirl speeds of the bladed rotor is then explained by classifying the whirling modes into three types according to their cause of manifestation and the frequency relationship: namely, original, coupled multi-blade, and conjugate whirling modes. (C) 2015 Elsevier Ltd. All rights reserved.
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