ABSTRACT
Equations of motion of the classically damped multi-degree-of-freedom (MDOF) systems can be transformed into a set of independent modal equations using the real-valued eigenvectors and eigenvalues of the undamped systems as was done in Chapter 1. However, in many real systems the modal equations are coupled by the nonclassical damping maxtrix[1]. In many cases, nonclassically damped systems can be approximated by a classically damped system without a significant loss of accuracy. On the other hand, there are important practical situations when the nonclassical nature of the damping matrix cannot be ignored. Such is the case when a structure is made up of materials with different damping characteristics in different parts. For example, a combined analytical model of a soil-structure system is nonclassically damped. Another example is a coupled structure-equipment (primary-secondary) system.
