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Natural Frequencies

 

Any physical structure can be modeled as a number of springs, masses, and dampers. Dampers absorb energy, but springs and masses do not. As we saw in the previous section, a spring and a mass interact with one another to form a system that resonates at their characteristic natural frequency. If energy is applied to a spring-mass system, it will vibrate at its natural frequency, and the level of the vibration depends on the strength of the energy source as well as the absorption or damping inherent in the system. The natural frequency of an undamped spring-mass system is given by the following equation:

where Fn = The natural frequency

k = the spring constant, or stiffness

m = the mass

From this, it is seen that if the stiffness increases, the natural frequency also increases, and if the mass increases, the natural frequency decreases. If the system has damping, which all physical systems do, its natural frequency is a little lower, and depends on the amount of damping.

The multitude of spring-mass-damper systems that make up a mechanical system are called "degrees of freedom", and the vibration energy put into a machine will distribute itself among the degrees of freedom in amounts depending on their natural frequencies and damping, and on the frequency of the energy source. For this reason, the vibration will not be uniformly distributed in the machine. For instance, in a machine driven by an electric motor, a major source of vibration energy is residual imbalance in the motor rotor. This will result in a measurable vibration at the motor bearings. But if the machine has a degree of freedom with a natural frequency close to the RPM of the rotor, its vibration level can be very high, even though it may be a long distance from the motor. It is important to be aware of this fact when evaluating the vibration of a machine -- the location of the maximum vibration level may not be close to the source of the vibration energy. Vibration energy frequently travels great distances along pipes, and can wreak havoc when it encounters a remote structure with a natural frequency near that of its source.





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