Matlab code for damping identification using energy ... - CFD4Aircraft

Analytical integration of experimental data
A single frequency sinusoidal function has been used to curve-fit the experimental measurements
in order to use an analytical integration of accelerations to obtain velocities and
displacements and to obtain an analytical expression of the integrals present in eq. (11).
Considering a single test with an excitation at frequency ω i , vector g i (t) taketheform
⎧
⎪⎨
g i (t) =
⎪⎩
0
0
g i (t)
0
0
0
0
0
0
0
⎫
⎪⎬
⎪⎭
(13)
The input is assumed to be perfectly sinusoidal, so the measurement of g i (t) from the force
transducer is fit to a harmonic function (figure 6) as
g i (t) =r i sin(ω i t)+s i cos(ω i t) (14)
by estimating the two coefficients r i and s i using least squares technique.
8
6
Measured
Sine-fit
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Force (N)
2
0
−2
−4
−6
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01
Time (s)
Figure 6: Typical measured and sine-fit force
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