2.1 Introduction

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In many vibration problems, the primary excitation force typically has a repetitive periodic nature, and

in some cases this periodic forcing function may be even purely sinusoidal. Examples are excitations due

to mass eccentricity and misalignments in rotational components, tooth meshing in gears, and

electromagnetic devices excited by AC or periodic electrical signals. In basic terms, the frequencyresponse

of a dynamic system is the response to a pure sinusoidal excitation. As the amplitude and

the frequency of the excitation are changed, the response also changes. In this manner, the response

of the system over a range of excitation frequencies can be determined. This represents the frequency

response. In this case, frequency ðvÞ is the independent variable and hence we are dealing with the

frequency domain.

2-1

© 2005 by Taylor & Francis Group, LLC

Frequency-domain considerations are applicable even when the signals are not periodic. In fact, a time

signal can be transformed into its frequency spectrum through the Fourier transform. For a given

time signal, an equivalent Fourier spectrum, which contains all the frequency (sinusoidal) components of

the signal, can be determined either analytically or computationally. Hence, a time-domain

representation and analysis has an equivalent frequency-domain representation and analysis, at least

for linear dynamic systems. For this reason, and also because of the periodic nature of typical vibration

signals, frequency-response analysis is extremely useful in the subject of mechanical vibrations. The

response to a particular form of “excitation” is what is considered in the frequency-domain analysis.

Hence, we are specifically dealing with the subject of “forced response” analysis, albeit in the frequency

domain.

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