TABLE OF CONTENTS In the previous four chapters of this book we have been concerned with the mathematical modelling of mechanical systems which results in a discrete set of time-differential equations. The object of the following five chapters will be to describe the mathematical procedures available to solve such analytical models and to develop the generic features of the dynamical responses, which are of major interest for the mechanical engineer. Because of the theoretical and practical importance of this field, broadly referred to as vibration theory, the literature on the subject is particularly abundant. Amongst the engineering oriented textbooks devoted mainly to linear vibrations, let us quote in particular [DEN 56], [ROC 71], [CLO 75], [MEI 67], [MEI 70], [BIS 60], [GIB 88], [DEN 89], [WEA 90], [GER 97].
Most material systems, initially at rest in a given state of equilibrium, are likely to vibrate as soon as they depart from it. Vibrations are said to be free whenever they are triggered solely by delivering initially some amount of energy to at least one degree of freedom of the system. Such free vibrations reveal themselves as extremely useful for investigating the response properties of the material system to any kinds of excitations, as will be illustrated in specific examples in the following chapters of this book. This chapter is devoted to the analysis of the free vibrations of SDOF systems, starting with the so-called linear or harmonic oscillator which is the simplest vibrating system. It serves as a convenient introduction...
