NODAL ENERGY WEIGHTED TRANSFORMATION: A NEW MISTUNING PROJECTION FOR FLADE™ SYSTEMS

摘要

In recent years, several researchers have developed reduced-order models (ROMs) to efficiently and accurately calculate the forced response of blisks with known small mistuning. Small mistuning consists of the small blade-to-blade structural differences which destroy the inherent cyclic symmetry of the structure. This paper presents a nodal energy weighted transformation (NEWT) which can be used to construct ROMs of mistuned blisks and dual flow path systems, such as Flade™ systems. The NEWT approach can be interpreted as a hybrid of two exisiting techniques: component mode mistuning, and the subset of nominal modes. Similar to previous methods, NEWT assumes that the mistuned modes of the system are a linear combination of tuned modes. However, NEWT differs from its predecessors in the blisk substructuring and in the mistuning projection. NEWT projects the (mass/stiffness) mistuning onto a select subset of single-sector tuned system (acutal or virtual) modes at optimally chosen nodal diameters (starting with the largest nodal diameter mode). Numerical results are presented for finite element models of a blisk and of a Flade system over multiple frequency ranges. These results show that ROMs based on NEWT have several attractive features: (a) the accuracy of the ROMs is comparable to other existing ROMs and can be improved by increasing the size of the projection mode subset; (b) no necessary modifications are needed to analyze Flade™ designs; (c) the response of all modes can be predicted well even if they are not blade dominated.