Expedient Estimation of the Maximum Amplification Factor in Damped Mistuned Bladed Disks

This paper focuses on the formulation and validation of a novel approach for the expedient estimation of the maximum amplification factor induced by mistuning in damped bladed disks. This computational approach is based on earlier analytical results yielding an upper bound of the maximum amplification factor in the limit of zero damping. Extensions of these results are derived first to broaden the applicability of the methodology. Next, the computational technique is described: it involves the components of one of the mode shapes of the mistuned disk and the associated frequency as the variables over which the optimization is carried out. Further, the initial guess for these variables is obtained from the analytical estimates of the upper bound. This approach removes the limitations of earlier analytical efforts, i.e. damping is considered, and the actual value of the maximum amplification factor and the corresponding mistuning of the blade properties are obtained. Limitations on the magnitude of the mistuning could also be considered in the algorithm if desired. This novel approach was applied for the parametric study of the maximum amplification factor as a function of damping in two single-degree-of-freedom per blade disk models as well as in a reduced order model of a blisk. The results obtained in connection with the two single-degree-of-freedom systems very closely match the global maxima predicted by an existing, more tedious algorithm introduced earlier to avoid convergence to one of the many local maxima known to often exist.