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## Section 14, Resonance in a Total System of Connected Parts Rather than in its Individual Parts

Individually resonant parts were described as producing "curling" mode shapes. Sometimes individual parts of a total system may not, within themselves, be resonant, but instead the "spring system" formed at the place where the parts are connected may be resonant. For example, view the diagram of the horizontal beam connected to a vertical column. Assume that the vertical column is not resonant. Also assume that the horizontal beam is not resonant. (No curling mode shape will be present.) However, at the place where the beam and column are connected, a spring system is formed. If this spring system has a resonance frequency close to a source frequency, it will resonate. It usually will resonate in such a way that the angle between the beam and the column will open and close a small amount at the resonant frequency. If vibrating but not resonant, the angle will remain constant. As this type of resonance does not reveal a curling mode shape, another method must be used for detection with vibration instruments. Notice that the pickups are placed as if they are both following the same circle. Another way of determining the positioning and direction for the pickups is to imagine that the pickups operate upon contact, such as would be true for contact microswitches.

Notice that the pickups were placed so that both microswitches closed as both the beam and column moved together -- in the same direction -- at the same time (in-phase). In the situation where there is resonance, the microswitch at the columns would close at the same instant in time that the microswitch at the beam would be open (180° out-of-phase). This portion is difficult to explain and difficult for many people to follow. Therefore a quick review may help.

In the first situation, both the horizontal beam and the vertical column are vibrating, but the phase relationships show that both points have their vibrations in-phase with each other. When the horizontal beam tilts clockwise, so does the vertical column, indicating that there is no resonance at the "spring system" formed at the juncture between the horizontal and vertical members. Putting a brace at X will have no effect. The second diagram's phase readings show each point vibrating opposite each other, indicating that a brace at X, between the horizontal beam and vertical column, is a good way to tune the structure's resonant frequency away from the vibration source's frequency, thereby eliminating the resonant condition.

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