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In recent years shipyards and shipowners have increasingly tuned in to the negative consequences of engine vibrations. Rohal'-Ilkiv, Model Predictive Vibration Control, 2 5 A system consisting of one vibrating mass has one natural frequency, but in many cases, in a controller it is sufficient to replace a continuous G. Still, it is important to review the dynamic analysis beyond this phenomenon, as the vibration of a mass-spring-damper system acts as a basis to understand more complex systems. The vibration of a point mass may be a simple phenomenon from the physical viewpoint. 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 and others. 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 and others.

This chapter gives only an outline of the usual problems encountered in vibration engineering and sets the ground for the upcoming discussion. There are numerous excellent books available on the topic of analyzing and solving problems of vibration dynamics. To introduce the reader into the theoretical basics of vibration dynamics, this chapter gives a basic account of engineering vibration analysis. We may acquire such mathematical models based on a first principle analysis, from FEM models and from experimental identification. Moreover, all active approaches, such as the model predictive control (MPC) of vibrations considered in this book require simplified mathematical models to function properly. All types of vibration control approaches-passive, semi-active and active- require analyzing the dynamics of vibrating systems. In other cases, eliminating vibrations may save human lives, a good example is the vibration control of civil engineering structures in an earthquake scenario. 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. 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. There are cases when vibrations are desirable, such as in certain types of machine tools or production lines. Vibrations are mechanical oscillations about an equilibrium position.

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