Numerous examples can be drawn from engineering applications for vibrating (dynamic) systems. An automobile subjected to road irregularities and engine excitations, a machine tool subjected to cutting forces, a steam generator of a nuclear power plant that undergoes flow-induced vibration, a high-rise building subjected to seismic motions at its foundation, an incinerator tower subjected to aerodynamic disturbances, an airplane excited by atmospheric turbulence and other aerodynamic forces, a gate valve of a fluid flow system under manual operation, and a heating, ventilating, and air conditioning control panel stressed because of vibrations in its support structure are such examples. Consider an aircraft in flight, as schematically shown in Figure 4.1. There are many

excitations on this dynamic system. For example, jet engine forces and control surface movements are intentional excitations, whereas aerodynamic disturbances are unintentional (and unwanted) excitations. The primary response of the aircraft to these excitations consists of motions in various degrees of freedom, including rigid-body and flexible-mode (vibratory) motions. Even though the inputs and outputs (excitations and responses) are functions of time,

they can also be represented as functions of frequency through Fourier transformation. The resulting Fourier spectrum of a signal can be interpreted as the set of frequency components that the original signal contains. As noted in Chapter 3, this frequencydomain representation of a signal can highlight many salient characteristics of the signal and, as a result, those of the corresponding dynamic system. For this reason, frequencydomain methods, particularly Fourier analysis, are used in a wide variety of applications such as data acquisition and interpretation, experimental modeling and modal analysis, machine monitoring and diagnostic techniques, signal and image processing and pattern recognition, acoustics and speech research, signal recognition, telecommunication, and dynamic testing for design development, quality control, and qualification of products. Many such applications involve the study of mechanical vibrations.