On the Attachment Location of Dynamic Vibration Absorbers

In mechanical engineering a commonly used approach to attenuate vibration amplitudes in resonant conditions is the attachment of a dynamic vibration absorber. The optimal parameters for this damped spring-mass system are well known for single-degree-of-freedom undamped main systems (Den Hartog, J. P., 1956, Mechanical Vibrations, McGraw-Hill, New York). An important parameter when designing absorbers for multi-degree-of-freedom systems is the location of the absorber, i.e., where to physically attach it. This parameter has a large influence on the possible vibration reduction. Often, however, antinodal locations of a single mode are a priori taken as best attachment locations. This single mode approach loses accuracy when dealing with a large absorber mass or systems with closely spaced eigenfrequencies. To analyze the influence of the neighboring modes, the effect the absorber has on the eigenfrequencies of the undamped main system is studied. Given the absorber mass, we determine the absorber locations that provide eigenfrequencies shifted as far as possible from the resonance frequency as this improves the vibration attenuation. It is shown that for increasing absorber mass, the new eigenfrequencies cannot shift further than the neighboring antiresonances due to interlacing properties. Since these antiresonances depend on the attachment location, an optimal location can be found. A procedure that yields the optimal absorber location is described. This procedure combines information about the eigenvector of the mode to be controlled with knowledge about the neighboring antiresonances. As the neighboring antiresonances are a representation of the activity of the neighboring modes, the proposed method extends the commonly used single mode approach to a multimode approach. It seems that in resonance, a high activity of the neighboring modes has a negative effect on the vibration reduction.