Dynamic Condensation of Nonclassically Damped Models
The static and dynamic condensation methods for undamped models have been described in Chapters 4, 5, and 6. These methods are also valid for proportionally or classically damped models because the proportional damping does not affect the normal modes of the undamped models. However, for many real-world structures and systems the proportional damping assumption is invalid. Examples of such cases are the structures made up of materials with different damping characteristics in different parts, structures equipped with passive (such as concentrated dampers) and active control systems, structures with layers of damping materials (such as smart structures), and structures with rotating parts (such as a rotor). For these structural systems, the normal modes with real values resulting from the corresponding undamped models cannot be used to uncouple the dynamic equations of the nonclassically damped model, the state vectors defined in state space are, hence, commonly used. The size of the system matrices in the state space will be doubled automatically compared to those defined in the displacement space. Therefore, the dynamic condensation technique becomes very important.
Unable to display preview. Download preview PDF.
- Bathe, KJ and Wilson, EL (1972) Large eigenvalue problems in dynamic analysis. Journal of Engineering Mechanics Division, 98 (EM6): 1471–1485.Google Scholar
- Carroll, WF (1999) A primer for finite elements in elastic structures. John Wiley and Sons, Inc., New York, NY.Google Scholar
- Huang, F and Gu, S (1993) A new approach for model reduction. Proceedings of the 11th International Modal Analysis Conference (Kissimmee, Florida), Society for Experimental Mechanics, Inc., Bethel, CT: 1572–1575.Google Scholar
- Qu, Z-Q (1998) Structural dynamic condensation techniques: Theory and applications. Ph.D. Dissertation, State Key Laboratory of Vibration, Shock and Noise, Shanghai Jiao Tong University, Shanghai, China.Google Scholar
- Qu, Z-Q and Selvam, RP (2000) Dynamic condensation methods for viscously damped models. Proceedings of the 18th International Modal Analysis Conference, (San Antonio, Texas), Society for Experimental Mechanics, Inc., Bethel, CT: 1752–1757.Google Scholar
- Qu, Z-Q, Selvam, RP, and Jung, Y (2003) Model condensation for nonclassically damped systems—Part II: Iterative schemes for dynamic condensation. Mechanical Systems and Signal Processing, 17(5): 10171032.Google Scholar
- Reddy, VR and Sharan, AM (1986) The static and dynamic analysis of machine tools using dynamic matrix reduction technique. Proceedings of the 4th International Modal Analysis Conference (Los Angeles, CA), Union College, Schenectady, NY: 1104–1109.Google Scholar