Introduction

The purpose of this chapter is to introduce damping forces into the structural equations of motion. Simply speaking, damping forces are internal or external friction forces that dissipate the energy of the structural system. Although damping forces are usually much smaller than their companion inertia and elastic forces, they nevertheless can have a significant affect on a vibratory motion, especially after many periods of vibration, or when the system is vibrating at one of certain important frequencies called the system's natural frequencies. This chapter describes various ways of characterizing damping and explains how the damping properties of a vibratory system can be measured. Solutions for the motion of one-DOF systems are presented for force free and certain applied forces to better explain the role that damping plays in structural systems.

Descriptions of Damping Forces

When an actual, force free, structural system is set in motion by means of initial deflections or initial velocities, or both, any point within the system generally vibrates with amplitudes that are very little different over short time intervals; that is, time intervals lasting typically five or fewer periods of the vibration. Figure 5.1(a) shows the calculated amplitude–time trace of such a vibration where the period t of the vibration is 1 sec and the initial displacement has a unit value. As will soon be seen, the sinusoidal expression that describes the force free motion of a one-DOF undamped system, has to be modified, in this case by an exponential multiplier, when one representative form of system damping is present.