Vibration analysis of a blade-disk system using transfer matrix method

Abstract

The vibration characteristics of a blade-disksystem are analyzed by using the transfer matrix method. The effects of stagger, pretist angle and rotational speed on the frequencies of the system are investigated. The geometric model considered comprises a disk clamped at the inner radius and having blades cantilevered at the disk outer radius. The disk is treated as a thin plate possessing rotational symmetry, and the blade is regarded as Euler-Bernoulli beam. The method is based on a substructuring technique, whereby the disk forms one substructure, and the blade forms the other substructure. First, for each of the two structures, the governing differential equations are transformed into a set of first-order equations and the transfer matrices are obtained by adopting the Runge-Kutta method. Next, the frequency equation of a blade-disk system is derived by combining the transfer matrix in both structures and applying the boundary conditions. The results show the influence of some important parameters of the blinded disks on its natural frequencies.