On Vibration Absorbers for Periodic Excitation

The dynamic vibration absorber is a commonly-used device for reducing the vibrations of a primary system subjected to harmonic excitation. In this paper, the absorber concept is generalized from harmonic to periodic excitation functions. A generalized measure of amplitude for periodic waveforms is defined and used to minimize the amplitude of the response through proper tuning of the absorber. It is determined that the best strategy in the case of a single, undamped absorber is to essentially tune the absorber to create an anti-resonance at the fundamental frequency of the excitation, just as would be done in the case of purely harmonic excitation. However, since higher harmonics are also present in the periodic excitation, an absorber so tuned cannot eliminate the vibrations of the primary system completely. It is therefore suggested to use multiple absorbers to create anti-resonances at the first few harmonics along with the fundamental frequency. Specifically, as shown in this paper, the use of dual absorbers permits substantial reduction in overall vibration levels in comparison with a single absorber of equal mass and thereby provides much improved absorber performance at the cost of relatively minor complication of the design.