29.3 VIBRATION CONTROL
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29.3.1 Isolation
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We have already done an example of using springs for damping, but, what are the practical options,
Springs - good for low frequencies because they are not massless as assumed. In fact, they have a damping ration of about 0.005. They are also well suited to harsh (long life) environments. They can have problems with "rocking".
Elastomeric Mounts - Rubber compounds best used in compression, also good for shear. Common ranges are 30-durometer for soft, low K rubber, to 80-durometer high K rubber (damping ratio about 0.05). These materials are good for high frequencies.
Isolation pads - Cork, felt, fiberglass. Frequencies start at low values (18Hz and up for fiberglass), common damping coefficients for cork and felt are .06.
Elastomers are not linear, so the spring constant will vary as they are loaded. Graphical solutions work well when finding spring constants. Some example curves are given below.
A solution can be done entirely with graphical methods. Manufacturers will provide graphs for specific materials and thicknesses.
Note: When designing you should always attempt to get the natural frequency at least three times lower than the frequency to be damped.
The same type of design techniques can be done with cork. (Note: they would have similar graphs to those for elastomers)
A set of specifications for an elastomer isolator are summarized below,
29.3.2 Inertial
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Inertial Blocks - Increase the mass of the object to decrease vibration amplitude, and decrease natural frequency.
Absorption - A secondary mass is added to draw off, and hopefully cancel out, vibrations
29.3.3 Active
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Active Systems - These systems are becoming very popular in new cars, etc. The example below uses a bellows with an adjustable pressure `P'. This pressure over area `A' gives a spring constant `K' and height `h'. If the pressure in the bellows is adjusted by the addition of gas, the spring constant will rise, tending to damp out different vibration frequencies (remember the ideal gas law `PV=nRT').
The `K' values vary significantly for Elastomers and Isolation pads as the load varies, therefore graphical values are often required to find the spring constants.
An example of a practical active vibration control system is piezo electric actuators mounted on the skin of an airplane wing. When unwanted vibrations occurred in the wings the actuators could have voltages applied to counteract the vibrations (both axial and torsional). [Mechanical Engineering, 1995]
Try problems V14, V15, V16, V17, V18, V19, V20, V21, V22, V23
References
Mechanical Engineering, "Controlling Wing Flutter With Miniature Actuators", Mechanical Engineering Magazine, ASME, 1995.
