Dynamics of Machines - Part II - IFS.pdf

(a) Amplitude [m/s 2 ]
x Signal 10−5
5
0
(a) in Time Domain − (b) in Frequency Domain
−5
0 5 10 15
time [s]
20 25 30
(b) Amplitude [m/s 2 ]
x 10−5
2
1
0
0 5 10 15 20 25
frequency [Hz]
Figure 12: Transient Vibration – Acceleration of the clamped-free flexible beam when two concentrated
masses m = m1 +m2 = 0.382 Kg are attached at its free end (L = 0.310 m) – Natural
frequency of the mass-spring system ”B”: 1.75 Hz.
• Damping Factor of the system ”B” – From fig.12, one gets: yo = 4.6 · 10 −5 [m/s 2 ], yN =
y54 = 1.0 · 10 −5 [m/s 2 ] and N = 54:
ξ =
1 +
1
2π·54 ln
1
2π·54 ln
4.6·10 −5
1.0·10 −5
4.6·10 −5
1.0·10 −5
• Equivalent Viscous Damping (d)
=
2 0.004498
≈ 0.005 (46)
1.000010
d = 2 · ξ · ωn · m = 2 · 0.005 · (1.75 · 2 · π) · 0.382 ≈ 0.04 [N · s/m]
21