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Chapter 3
Fundamentals of Structural Dynamics

Excerpt

In the presence of damping but without external forces, the solution to the linear vibration problem takes the form (compare with free vibration in Chapter 2)

y=a0eiΩte(c2m)t
where Ω, the natural frequency of the damped point-mass spring system, is given by:
Ω=ω02c24m2

When the damping coefficient c > 2m ω0, energy dissipation is so large that vibration motion cannot be sustained. The motion becomes that of the exponentially decay type instead of vibration. The value of c at which this happens ( cc = 2mω0) is called the critical damping. The more commonly used damping ratio is the damping coefficient expressed as a fraction of its value at critical damping

ζ=ccc,cc=2mω0

In terms of the frequency (in Hz) and the damping ratio, the damped natural frequency is given by:

f0=f01ζ2

  • Summary
  • Nomenclature
  • 3.1 The Equation of Motion with Damping but no External Force
  • 3.2 Forced-Damped Vibration and Resonance
  • 3.3 Transient Vibrations
  • 3.4 Normal Modes
  • 3.5 Structural Dynamics
  • 3.6 Equation for Free Vibration
  • 3.7 Mode-Shape Function Normalization
  • 3.8 Vibration Amplitudes, Bending Moments and Stresses
  • Example 3.1
  • 3.9 Equivalent Static Load Method
  • Example 3.2
  • 3.10 Power Dissipation in Vibrating Structures
  • References

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