Since all dynamic characteristics of rotor systems are closely related with rotor rotations, the directivity of modes is very important in rotor dynamics. But the classical modal testing theories which have been applied to nonrotating structures were often applied to rotor systems. Whereas the dynamic characteristics in negative frequency region have no meanings in nonrotating stuctures, the dynamic characteristics of rotor systems in the negative frequency region which are different from those in the positive frequency region have significant physical meanings. Here a new modal testing theory is proposed to separate the rotor vibration into positive and negative frequency regions. In particular, the amplitude and directivity variations of frequency response functions in positive and negative frequency regions are discussed when using complex modal displacement. And a method to identify the directivity of modes such as forward and backward is suggested using the frequency response function obtained by the proposed modal testing theory. The whirl directions of forced responses related with the directivity of modes are also discussed. In addition, even if the anisotropy in bearings and the effects of gyroscopic moments are permitted, the relations between the right and left eigenvectors of general damped anisotropic rotor systems are evaluated under some practical conditions. If the relations between the right and left eigenvectors are given, the necessity of additional modal testing to identify the adjoint modal parameters is relaxed.
A modified complex modal testing technique for a rotating tire with a flexible ring model