Dynamic Reduction in Rotor Dynamics by the Finite Element Method

The use of dynamic reduction of finite element matrices in rotor dynamics analysis is shown to offer advantages of computational efficiency and modeling accuracy. Solution procedures and sample results for comprehensive rotor dynamics program for design purposes are presented. The basic reduction approaches have been extensively used in general structural analysis. Application to rotor dynamics requires an extension to account for skew-symmetric gyroscopic matrices. Dynamic reduction allows the analyst to discretize the rotor to a convenient level of detail, and then retain only enough degrees of freedom to adequately describe rotor behavior. Subsequent assembly of reduced shaft matrices with bearing matrices at a given speed allows various types of analysis to be conducted including: critical speed, damped eigenvalue-eigenvector, synchronous response, and transient solution. The computer solution time is significantly reduced because of the reduced number of degrees of freedom, with little sacrifice in accuracy for the lower modes of usual interest. The repeated use of reduced rotor matrices throughout a speed range also provides reduced computer costs.