Dynamics of Machines - Part II - IFS.pdf

(a) Amplitude [m/s 2 ]
(b) Amplitude [m/s 2 ]
0.5
0
−0.5
x Signal 10−4
1
(a) in Time Domain − (b) in Frequency Domain
−1
0 5 10 15
time [s]
20 25 30
x 10−5
2.5
2
1.5
1
0.5
0
0 5 10 15 20 25
frequency [Hz]
Figure 13: Free vibration – Spring-mass systems with 1 D.O.F. Two masses m = m1 + m2 =
0.382 Kg fixed at the middle of the beam L1 = 0.155 m, resulting in a system ”B” natural
frequency of 3.81 Hz
• Damping Factor of the system ”B” – From fig.13, one gets: yo = 0.95 · 10 −4 [m/s 2 ],
yN = y34 = 0.50 · 10 −4 [m/s 2 ] and N = 34:
ξ =
1 +
1
2π·34 ln
1
2π·34 ln
0.95·10 −4
0.50·10 −4
0.95·10 −4
0.50·10 −4
• Equivalent Viscous Damping (d)
=
2 0.003029
≈ 0.003
1.000005
d = 2 · ξ · ωn · m = 2 · 0.003 · (3.81 · 2 · π) · 0.382 ≈ 0.05 [N · s/m]
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