《Basics of Vibration Dynamics》.pdf
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Chapter 2
Basics of Vibration Dynamics
Vibrations are mechanical oscillations about an equilibrium position. There are cases
when vibrations are desirable, such as in certain types of machine tools or production
lines. Most of the time, however, the vibration of mechanical systems is undesirable
as it wastes energy, reduces efficiency and may be harmful or even dangerous. For
example, passenger ride comfort in aircraft or automobiles is greatly affected by
the vibrations caused by outside disturbances, such as aeroelastic effects or rough
road conditions. In other cases, eliminating vibrations may save human lives, a good
example is the vibration control of civil engineering structures in an earthquake
scenario.
All types of vibration control approaches—passive, semi-active and active—
require analyzing the dynamics of vibrating systems. Moreover, all active approaches,
such as the model predictive control (MPC) of vibrations considered in this book
require simplified mathematical models to function properly. We may acquire such
mathematical models based on a first principle analysis, from FEM models and
from experimental identification. To introduce the reader into the theoretical basics
of vibration dynamics, this chapter gives a basic account of engineering vibration
analysis.
There are numerous excellent books available on the topic of analyzing and solving
problems of vibration dynamics. This chapter gives only an outline of the usual
problems encountered in vibration engineering and sets the ground for the upcoming
discussion. For those seeking a more solid ground in vibration mechanics, works
concentrating rather on the mechanical view can be very valuable such as the work
of de Silva [10] and others [4, 22]. On the other hand, the reader may get a very good
grip of engineering vibrations from the books discussing active vibration control
such as the work of Inman [21] and others [15, 18,
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