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## Section 1, Plotting the Mode Shapes from Point-to-Point Amplitude Readings to Determine whether a Part is Resonant

When a part or section, such as a length of pipe between supports is not resonant, the vibration mode shape is relatively flat or straight. When the part is resonant, the same vibrating part will show a relatively large "curl." When a part is not resonant, the mode shape may exhibit a slight amount of "curl" but compared to when it is resonant, is relatively straight. The following method enables you to determine whether a part is resonant. It is an especially valuable method for determining resonance of a machine's exposed non-rotating parts when the machine cannot be readily shut down for shaker or bump tests.

This method easily reveals which specific section of pipe, pedestal, floor or beam is resonant as well as indicating just which part of a welded steel base should be detuned. It is also used in when resonance is suspected but not actually occurring, thereby saving the expense and embarrassment of futilely altering a part to change its resonance frequency.

Another common situation occurs when resonance is suspected in a pipe due to its extremely high vibration amplitude as compared to the vibration at the bearings. The longer, more flexible section is usually most suspect. Yet after plotting the mode shapes of each section, it may be found that it is not the long, flexible section that is resonant, but instead the short, tapered adapter from the pump to the pipe. (Such short, rigid parts, if resonant, are usually resonant to higher frequency vibrations such as vane pass frequency or gearmesh frequency.)

[graphic coming soon]

Note that a resonant part has places of maximum amplitude and curl called "antinodes" and points of almost no amplitude called "nodes." Adjacent antinodes vibrate 180° opposite each other. When an antinode is deflecting in one direction, the adjacent antinodes are deflecting in the opposite direction. This causes a flexing back and forth that is concentrated at the nodes. If continued long enough, the part will eventually crack at one or more of the nodes. For very severe vibration that is close to the peak resonant frequency, the nodes should be very sharp, that is, concentrated in a very small part of the length. This could result in a crack forming in a very short time, such as a few weeks to a few months. For extremely large vibration amplitudes and very sharp nodes, cracks sometimes develop in a few days. Parts that are only partially resonant will have antinodes of smaller amplitudes and less pronounced curl. Nodes will be present but not as sharp. Cracks most likely will develop over a much longer span of time such as more than a year. The reason why resonant or partially resonant parts may not produce cracks is that the resonance magnified vibration often causes other problems to occur first, forcing corrections of vibration at its source.

Parts with large vibration amplitudes that are not resonant, will show a slight amount of curling but no easily discernable nodes. One way to determine if a part with some mode shape curl is resonant or not, is to examine it for nodes at the ends of the mode shape. Resonant parts will show relatively sharp nodes at the ends (compared to the amplitudes at the antinodes). Non-resonant parts will have much larger amplitudes at the ends compared to the amplitude at the largest section of curl.

Determine mode shapes only for those parts that are vibrating at higher amplitudes than at the machine's bearing with the highest amplitude. Non-resonant parts usually have much smaller amplitudes.

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