Abstract：To investigate dynamic response behaviors of rotating machinery subjected to seismic or non-contact underwater explosion shock, we always start from the study of rotor-bearing systems representing those machines under base motion. Due to the gyroscopic effect and the interaction between rotor and bearing, system matrixes are nonsymmetric, so, conventional mode-superposition method cannot be applied to solve the system motion equations. Numerical direct time-integration methods are now used commonly obtaining a transient response of rotor-bearing systems, but compared to linear superposition method, they require more computing resources. For the above reason, a superposition method in complex domain was proposed. With no need to decouple equations, linear superposition computation of responses can still be performed just like that in the conventional mode-superposition method. Firstly, shock excitation and response were both expanded into a complex form of Fourier series, including forward and backward rotating items. Characteristic equations were obtained by the fact that coefficient matrixs of same rotating frequency are equal. Characteristic equations were then rewritten into simple pencil of matrix’ latent value equations. Inverse matrix of which elements are called “ Frequency Response Coefficient” of the pencil of matrix was calculated out by using its right and left latent vectors which were normalized. Responses in each frequency were obtained by the product of the inverse matrix and shock excitation, and then synthesized into overall responses of the system. An engineering example is to compare the proposed method and the results of numerical integration methods, comparative analysis shows that the proposed method to meet the engineering requirements, and can be used as a universal method of shock response and transient response computation of rotor systems.
2011, Vol. 30 
