TABLE OF CONTENTS The focus of this textbook is on the vibrations of engineering structures, not mechanisms. However, this chapter focuses on pendulums as representative of mechanisms. Pendulums are rarely a part of an engineering structure. [1] However, because the motions of pendulums are familiar to everyone, they do provide a comparatively simple means for both visualizing and explaining some basic aspects of more general vibratory systems. Pendulums also provide an opportunity to consolidate the lessons on dynamics set forth in the first chapter without the complication of dealing with flexible structures. As an aside, pendulums also provide a relatively simple introduction to the quite challenging topic of nonlinear vibrations. Thus, despite their limited relevance to engineering structures in general, this introductory study of structural dynamics begins with the study of the back-and-forth motion of pendulums.
The static equilibrium position (SEP) of any dynamical system is the deflected position of that system in response to all the applied static loads and their support reactions, if any. A stable pendulum system is defined as any system that, when displaced from its static equilibrium position, tends to return to that SEP as a result of the presence of a gravitational force field or other force field. An example of body forces other than gravitational forces that stabilize a structural system is the centrifugal force field acting on a rotating helicopter blade. Consider a rotating helicopter blade that is unrestrained at its outer end and has a single, horizontal hinge line that...
