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). 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, anti nodal 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 anti resonances due to interlacing properties. Since these anti resonances depend on the attachment location, an optimal location can be found. A procedure is described that yields the optimalabsorber location. This procedure combines information about the eigenvector of the mode to be controlled with knowledge about the neighboring anti resonances. As the neighboring anti resonances are a representation of the activity of the neighboring modes, the proposed method extends the commonly used single mode approach to a multi mode approach. It seems that in resonance, a high activity of the neighboring modes has a negative effect on the vibration reduction