TABLE OF CONTENTS Damping was introduced in Chapter 1 as one of the 'building blocks' making up the systems we deal with in structural dynamics, and some of the ways in which it can be generated were discussed. The effects of linear, viscous, damping, on the response of a single-DOF system, were discussed in Chapters 2, 3 and 4. In this chapter, we also look at another form of linear damping, hysteretic damping, and compare it with viscous damping. We then discuss how damping is related to energy loss; the different ways in which damping is quantified; two common forms of non-linear damping; and methods of approximating them with linear models. Damping in multi-DOF systems is discussed, with those systems, in Chapter 6.
These are the two linear damping models, and so far we have only discussed the viscous model. Hysteretic damping is sometimes called structural or solid damping, so unfortunately, the phrase 'structural damping' can mean either the damping (of any kind) in a structure or hysteretic damping. Therefore, only the latter term will be used here.
Comparing viscous and hysteretic damping is only possible by comparing frequency responses, since systems with hysteretic damping do not have an analytic transient response.
We first rearrange the equation of motion of a single-DOF system with viscous damping, into a slightly unusual form more easily compared with that for a system with hysteretic damping, as follows.
The familiar system shown in Fig. 5.1 has the equation...
