Dynamics of Machines - Part II - IFS.pdf
Dynamics of Machines - Part II - IFS.pdf
Dynamics of Machines - Part II - IFS.pdf
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||y 1 (ω)|| [m/N]<br />
Phase [ o]<br />
Excitation on Point 1 and Response <strong>of</strong> Point 1<br />
0.25<br />
0.2<br />
0.15<br />
0.1<br />
0.05<br />
−100<br />
−150<br />
−200<br />
−250<br />
−300<br />
0<br />
0 2 4<br />
Frequency [Hz]<br />
6 8<br />
0<br />
−50<br />
−350<br />
0 2 4<br />
Frequency [Hz]<br />
6 8<br />
||y 2 (ω)|| [m/N]<br />
Phase [ o]<br />
Excitation on Point 1 and Response <strong>of</strong> Point 2<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
−100<br />
−150<br />
−200<br />
−250<br />
−300<br />
0<br />
0 2 4<br />
Frequency [Hz]<br />
6 8<br />
0<br />
−50<br />
−350<br />
0 2 4<br />
Frequency [Hz]<br />
6 8<br />
Figure 26: Forced Vibration – Theoretical Frequency Response Function (FRF) <strong>of</strong> the clampedfree<br />
flexible beam when two concentrated masses m = m1 + m2 = 0.382 Kg are attached at its<br />
free end (L = 0.610 m) and two additional masses m = m1 + m2 = 0.382 Kg are attached at its<br />
middle (L = 0.310 m) – Natural frequencies <strong>of</strong> the 2. D.O.F. mass-spring system ”A”: 0.81 Hz<br />
and 5.56 Hz.<br />
1.7.8 Understanding Resonances and Mode Shapes using your Eyes and Fingers<br />
• Understanding the ”90 Degree Phase between excitation force and displacement response<br />
while in Resonance” using tactile senses. In other words, understanding ”Zero Degree Phase<br />
between the excitation force and velocity response while in resonance” using tactile senses.<br />
• Visualization <strong>of</strong> the participation <strong>of</strong> modes shapes in the transient response – Visualization<br />
using your eyes! Transient motion <strong>of</strong> the physical system excited with different initial<br />
conditions by using your fingers!<br />
43