Page 47 - Rotating Machinery Pratical Solutions to Unbalance and Misalignment

Resonance and Beat Frequencies

Equation (3.1) yields f =22.36 Hz. This is only a 10.6% change in
frequency for a 40% increase in mass.
In most cases, adding mass to a component is not practicable
and the component must be stiffened.

Example 3.2
In the system described in Example 3.1, the stiffness of the
object is increased by welding a bracket in place. The bracket
weighs 1 pound and increases the stiffness to 28,750 lb./ft. What
is the resulting new natural frequency?
The new mass is 21/32.2 or .6522 pounds. Using the new
mass and the new constant k, and substituting into Equation (3.1)
yields f = 33.42 Hz..
This change in the stiffness resulted in a 33.68% change in the
natural frequency of the object. This frequency change would be
adequate to keep the object from being excited by an external force
at 25 Hz.
Of course, the best way to solve the situation is to remove the
source of the original vibration. Generally, the vibrating source is
operating at a fixed speed and a significant reduction in its driving
force cannot be accomplished. Vibration isolators or additional
dampening can sometimes be added.
Most vibrations in machine elements are of the damped type
as illustrated in Figure 3-3. Although most parts do not have damp-
ers or shock absorbers attached to them, contact with other compo-
nents of a machine has the effect of dampening the vibration.

Figure 3-3. Damped Vibration