ABSTRACT
The design of structural control systems requires a deep knowledge of structural dynamics, particularly regarding the theory of structural vibrations. This chapter covers the mathematical fundamentals to analyze structural vibrations. The degree-of-freedom of a system is defined as the number of independent vectors required to define the motion characteristics of a system. Using simple single-degree-of-freedom systems, this chapter introduces a classification of structural responses considering their damping characteristics. Furthermore, the initiation process of the vibrations is distinguished as free and forced. Frequency- and time-domain based methods are described for the calculation of such vibrations. The fundamentals of single-degree-of-freedom systems are enhanced to multi-degree-of-freedom systems and the basic theory of modal analysis is presented for the computation of these systems. A general overview of damping models is given, which are relevant for the mathematical description of the material behavior of vibration control devices. Finally, the topic of nonlinear vibrations is covered, which can occur particularly in controlled structures.
