Introduction to Aircraft Aeroelasticity and Loads

1

Vibration of Single Degree of Freedom Systems

In this chapter, some of the basic concepts of vibration analysis for single degree of freedom (SDoF) discrete parameter systems will be introduced. The term ‘discrete (or sometimes lumped) parameter’ implies that the system is a combination of discrete rigid masses (or components) interconnected by flexible/elastic stiffness elements. Later it will be seen that a single DoF representation may be employed to describe the behavior of a particular characteristic (or mode) shape of the system via what are known as modal coordinates. Multiple degree of freedom (MDoF) discrete parameter systems will be considered in Chapter 2. The alternative approach to modelling multiple DoF systems, as so-called ‘continuous’ systems, where components of the system are flexible and deform in some manner, is considered later in Chapters 3 and 4.

Much of the material in this introductory part of the book on vibrations is covered in detail in many other texts, such as Tse et al. (1978), Newland (1987), Rao (1995), Thomson (1997) and Inman (2006) and it is assumed that the reader has some engineering background so should have met many of the ideas before. Therefore, the treatment here will be as brief as is consistent with the reader being reminded, if necessary, of various concepts used later in the book. Such introductory texts on mechanical vibration should be referenced if more detail is required or if the reader's background understanding is limited. ...