《Basics of Vibration Dynamics》.pdf

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,