340 - Analysis of nonlinear forced vibration using component mode synthesis method
Kawamura S., Naito T., Minamoto H., Zahid H.
Abstract
Recently, the nonlinear vibration analysis becomes more important from the viewpoint of machine condition monitoring and diagnosis. Usually, the equation of motion with nonlinear properties is constructed, for example, using F.E.M., then the equation is transformed into modal equation with a few modal responses by the modal analysis technique. After that, the nonlinear vibration is calculated by the direct integration, the method of multiple scales, harmonic balance method and so on. However, when the system has huge degrees of freedom, the eigenvalue analysis needs much computer storage and calculation time. Because of the reason, the component mode synthesis method has been developed, but the method can be only applied for the linear system in principle. In this paper, an analytical approach for nonlinear forced vibration of multi degrees of freedom system is proposed using the component mode synthesis method. The whole system is divided into some components and a nonlinear modal equation of each component is derived using the unconstrained vibration modes. The modal equations of all components and the conjunction conditions are solved simultaneously, and then the modal responses of components are derived. Finally, the dynamic responses of the whole system can be obtained. The degrees of freedom of modal equations can be reduced when the lower vibration modes are only adopted in each component. As a numerical example, a simple five degrees of freedom system is considered, in which all spring have cubic type nonlinearity. The system is divided into two components of three degrees of freedom system and the proposed method is applied. As a result, it is shown that even if the first vibration mode of each component is only adopted, the dynamic response near the first resonance can be accurately obtained.
Citation
Kawamura S.; Naito T.; Minamoto H.; Zahid H.: Analysis of nonlinear forced vibration using component mode synthesis method, CD-ROM Proceedings of the Thirtheenth International Congress on Sound and Vibration (ICSV13), July 2-6, 2006, Vienna, Austria, Eds.: Eberhardsteiner, J.; Mang, H.A.; Waubke, H., Publisher: Vienna University of Technology, Austria, ISBN: 3-9501554-5-7
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