Perturbation theory in modal analysis of mistuned rotors

Abstract

In this paper, the change of natural frequencies and the mode shapes of bladed disk assembly due to mistuning is investigated by applying perturbation theory. It is well known that for rotor assemblies the different properties of each blade, which is called mistuning, affect greatly the structure behavior. Thus, the effect of mistuning on the vibration of bladed disk has been studied for more than 30 years. Many techniques have been developed to understand the vibration of mistuned rotors as well as to reduce the computational time for mistuning simulation or statistical analysis. However, in this paper a different approach is carried out. Two kinds of perturbation analysis are presented. The first perturbation analysis is applied by using ‘standard’ perturbation technique. By employing this technique it can be shown that the computed natural frequencies and corresponding modes by using subset of nominal modes (Yang and Griffin, 1999) can be improved. The advantages and disadvantages of this technique are discussed as well. The second analysis is performed on basis of relative perturbation theory. The application of relative perturbation theory makes it possible to estimate the bounds of modal characteristics of mistuned bladed disk. A simple model of mistuned bladed disk assembly and a turbine model are given as numerical examples to verify the techniques. Even though the solution using relative perturbation theory can very well set the bounds of natural frequencies, this approach cannot fully capture the characteristic of blade modes. Therefore, the new progress in this field is still being studied.

Keywords:

• Perturbation
• mistuned rotor
• modal characteristics