Isolation of bending vibration in a beam structure with a translational vibration absorber and a rotational vibration absorber

One drawback of the traditional dynamic vibration absorber is that it can only absorb the vibration of a continuous structure such as a beam at the point to which it is attached. In this article, it is proved that if damping in a vibrating beam structure is negligible, a translational dynamic absorber used in combination with a rotational dynamic absorber can absorb both translational and rotational motions for part of a vibrating beam subjected to harmonic excitation. An analytical model based on Euler-Bernoulli beam theory is constructed for a beam under partially distributed loading, and it is proved theoretically that the two absorbers can not only absorb vibration in the unforced portion of the beam, but can also isolate vibration in the portion under direct excitation. Two numerical examples are given for illustration, and some useful applications of the absorbers are discussed.