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.