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Chapter 2
The Kinematics of Vibration and Acoustics

Excerpt

The motion represented by the equation

y(t)=a0cosωt+b0sinωt
or, in more compact complex variable notation,
y(t)=a0eiωt
is called simple harmonic motion. Most vibrations and noise we encounter belong to the category of linear vibration and consist of a linear combination of simple harmonic motions of different amplitudes, frequencies and phases. The frequency of a point mass-spring system is given by:
ω=kmradians
The frequency in cycles/s, or Hz, is related to the frequency in radians/s by,
f=ω2πHz
The instantaneous velocity and acceleration of a vibrating point mass is given by:
V(t)=(t)=iωy(t)
α(t)=ӱ(t)=ω2y(t)
The velocity of propagation of a wave is given by:
c=fλ
Vibrations can be represented in the time domain (time histories) or in the frequency domain (power spectral densities). Both contain the same information.

  • Summary
  • Nomenclature
  • 2.1 Introduction
  • 2.2 Free Vibration and Simple Harmonic Motion
  • 2.3 Linear Vibration and Circular Motion
  • 2.4 Vibration Measurement
  • 2.5 Time Domain Representation of Vibration
  • 2.6 Superposition of Sinusoidal Waves
  • 2.7 Random Vibration and Noise
  • 2.8 Frequency Domain Representation of Vibration
  • 2.9 Traveling Waves
  • 2.10 Propagation of Sound Waves
  • Example 2.1: Tapping Wave Forms from Two Piston Lift Check Valves
  • 2.11 Energy in Sound Waves
  • 2.12 Threshold of Hearing and Threshold of Pain
  • 2.13 The Logarithmic Scale of Sound Intensity Measurement—The Decibel
  • 2.14 The Decibel Used in Other Disciplines
  • 2.15 Case Studies
  • Case Study 2.1: Forced Vibration of Nuclear Reactor Components by Coolant Pump-Generated Acoustic Load
  • Case Study 2.2: Detecting Internal Leaks in a Nuclear Plant
  • References

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