Master Thesis - OUFTI-1

• The logarithmic decrement method: This method is a time domain approach.
It calculates damping based on the free decay of oscillations in the structure using
Equation 4.2.6.
( )
xn
∆ = ln = 2 π ζ
x n+1
√ ⇒ ζ = 1
√
1 − ζ
2
1 + ( 2 π
∆
) 2
(4.2.6)
where ∆ is the logarithmic decrement between times n and n + 1, x i is the response
of the structure at a given time i and ζ is the damping factor.
If the assumption of low damping can be applied, this equation is greatly simplied.
This simplication is presented in Equation 4.2.7.
∆ ≈ 2 π ζ ⇒ ζ = 2 π
∆
(4.2.7)
• The peak-amplitude method: This method is a frequency domain approach. It
calculates damping based on the Frequency Response Function (FRF) of the structure.
Once the FRF is obtained, the response at the half-power points (illustrated in
Figure 4.10) is measured and the damping can be calculated as shown in Equation
4.2.8.
Figure 4.10: Illustration of the peak-amplitude method [53]
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