Page 50 - Rotating Machinery Pratical Solutions to Unbalance and Misalignment
P. 50
Rotating Machinery: Practical Solutions
Where:
L = length
n = 1,2,3,4…
The velocity of the wave can be expressed as:
v = fλ (3.4)
Since the speed of compression waves is related to density
and the elasticity of a material, the velocity may also be expressed
as:
v = (E/p) .5 (3.5)
Where:
E = Modulus of elasticity
p = Mass density
This equation states the velocity is equal to the square root of the
modulus of elasticity divided by the mass density.
In Figure 3-7, a simply supported pipe is vibrating at its
natural frequency. Note that at the two supports, the amplitude is
zero. These are referred to as node points. In this case, the center
has the greatest amplitude and is referred to as an anti-node.
Figure 3-7. Pipe Vibrating at its Natural Frequency
Example 3.3
The pipe in Figure 3-7 was struck near its center and was
found to vibrate at a frequency of 2 Hz. The distance between
