A multiple harmonic balance method for the internal resonant vibration of a non-linear Jeffcott rotor

A multiple harmonic balance method is presented in this paper for obtaining the internal resonant steady state vibration of a Jeffcott rotor with a piecewise-linear non-linearity at the bearing support. The method utilizes the hypertime concept, which isolates each frequency component of a response into pseudo-time domains. Explicit Jacobians are derived to obtain stable convergence solutions in the iteration process. The frequency components of the non-linear restoring force part are analytically expressed from those of the displacement part, using the Galerkin technique to guarantee a convergent solution. As the method utilizes general and systematic computational procedures, it can be applied to analyze the multi-tone or combination-tone responses fbr higher-dimensional non-linear systems such as multi-disk rotors or automotive drivelines with multiple excitational inputs. To demonstrate the accuracy and effectiveness of the proposed method, various simulation results are studied and the results of multiple HBM are compared with those from numerical integration. (C) 1997 Academic Press Limited.