Theory of the Damped Dynamic Vibration Absorber for Inertial Disturbances

If a mass which is mounted flexibly is set into forced vibrations by a harmonic force having an amplitude which does not vary with frequency, a damped dynamic vibration absorber may be designed to reduce the vibrations to some preassigned amplitude, regardless of the range over which the frequency of the disturbing force may vary. The theory of this type of vibration absorber, together with valuable discussion, has been given in a paper by Ormondroyd and Den Hartog, and is readily available in Den Hartog’s text on mechanical vibrations. In this paper the author presents a similar analysis for the case in which the amplitude of the disturbing force varies as the square of its frequency. For lack of a better name, this will be referred to as the case of “inertial disturbance.” Such cases are of considerable practical importance. For example, disturbances due to unbalance in rotating machinery are of this type. In some cases, such as those in which the unbalance varies with temperature, it may be impractical or impossible to secure perfect or nearly perfect balance, and a vibration absorber, designed on the basis of the analysis to be presented, may offer a suitable remedy. A practical example of this nature is given. The analysis follows a pattern similar to that given by Den Hartog, but enough of the details are different to warrant an extended treatment.