2 Frequency-Domain Analysis Clarence W. de Silva

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The University of British Columbia

2.1 Introduction ........................................................................... 2-1

2.2 Response to Harmonic Excitations ...................................... 2-2

Response Characteristics † Measurement of Damping Ratio

(Q-Factor Method)

2.3 Transform Techniques ......................................................... 2-14

Transfer Function † Frequency-Response Function

(Frequency Transfer Function)

2.4 Mechanical Impedance Approach ...................................... 2-25

Interconnection Laws

2.5 Transmissibility Functions .................................................. 2-31

Force Transmissibility † Motion Transmissibility †

General Case † Peak Values of Frequency-Response Functions

2.6 Receptance Method ............................................................. 2-37

Application of Receptance

Appendix 2A Transform Techniques ................................. 2-40

Summary

This chapter presents the frequency-domain analysis of mechanical vibrating systems. In the frequency domain,

the independent variable is frequency. The response of a vibrating system to harmonic excitations under various

levels of damping (overdamped, underdamped, and critically damped) is analyzed. Frequency transfer function

techniques including impedance, mobility, force transmissibility, motion transmissibility, and receptance are

studied. Transform techniques (Fourier and Laplace) are applicable in the frequency-domain analysis. The

Q-factor method of measuring damping is derived. Component interconnection laws are established for frequencydomain

analysis. The emphasis is on single-degree-of-freedom (single-DoF) systems.

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