Identification of travelling wave modes in rotating disk via directional spectral analysis

Abstract

As the modern rotating disks have a tendency of being operated at higher speed and designed to be lighter and thinner, the knowledge of the dynamic behavior becomes more and more important because of increasing requirement in accuracy and reliability. Modal testing of stationary structures has provided a major contribution to our efforts to understand and to control many vibration phenomena encountered in practice. Unlike nonrotating structures, however, modal distribution in a rotating disk is characterized by pairs of waves propagating in opposite directions along the periphery of the disk. The waves propagating in the direction and in the opposite direction of disk rotation are called the forward and backward travelling waves, respectively. Although the presence of backward and forward travelling wave modes in rotating disks has been extensively investigated in the literature, the modal characteristics such as the directivity of the modes and the diametrical node numbers have been seldom emphasized because of the inherent limitation in the analysis of conventional frequency response functions. The primary objective of this work is to develop a systematic method to separate the forward and backward travelling wave modes and to identify the diametrical node numbers in rotating disk because the modal distribution of rotating disk is very changed due to the diametrical node number. In this work, the modal equation associated with each complex wave coordinates is derived using modal analysis and the complex (conjugate) wave directional frequency response function which contains the information of backward and forward travelling wave (conjugate) modes is obtained. Then, conventional frequency response function for isotropic rotating disk in the physical domains is derived using complex wave directional frequency response function. It is confirmed that the derived conventional frequency response function well represents the dynamic characteristics of rotating disk ...