Hybrid reduction of mistuned bladed disks for nonlinear forced response analysis with dry friction

An efficient model order reduction technique for forced vibration analysis of a mistuned bladed disk with friction contact is presented. The present method applicable for small blade-to-blade mistuning, provides significant reduction in time without loss of accuracy for the nonlinear statistical analysis of mistuned bladed disks. This is achieved by obtaining a reduced order model of the mistuned bladed disks without generating its stiffness and mass matrices and considering the effect of mistuning on the static modes used in the reduction. This new approach can be interpreted as a hybrid of two existing techniques: Component mode mistuning (CMM) and a Dual model order reduction technique. The Dual method is a free interface based Component Mode Synthesis (CMS) method whose unique formulation makes it appropriate for mistuning analysis. The reduction basis in Dual approach includes free interface normal modes and residual flexibility attachment modes of mistuned bladed disk. These modes are computed using CMM and a proposed approximate approach, respectively. The resulting governing equation are solved in the frequency domain using Harmonic Balance method while contact forces are computed by an Alternating Frequency–Time method and a node-to-node 3D coupled contact model. The method is applied to a simplified shrouded turbine bladed disk, the results demonstrate the accuracy of the proposed method and the importance of tackling friction nonlinearity and mistuning simultaneously.