The system loss factor in sound and vibration

Abstract

In 1930, Kimball wrote a paper entitled "The damping factor in vibrations" that appeared in the journal Product Engineering. That paper proposed a damping factor based on the decrement of a vibrating system with exponential decay. Kimball showed that the proposed damping factor was proportional to the ratio of the energy dissipated per cycle to the total vibrational energy. The total vibrational energy was defined as the maximum potential energy over a cycle. Since that time, the definition of total vibrational energy has been more thoroughly examined because the total vibrational energy varies within a cycle due to damping. In this presentation, a new definition is proposed that defines the total vibrational energy as the temporal average of the total vibrational energy over a cycle. This definition has the advantage of reducing the system loss factor to the modal loss factor under certain limits. Since 1930, Kimball's damping factor has appeared in various forms under various names, the most common of which is the system loss factor. This presentation discusses these appearances in order to understand energy losses in dynamic systems caused by a wide array of physical mechanisms. The presentation concludes with a discussion of the system loss factor in present-day numerical simulations, highlighting its independence from eigenvalue information. [Work supported by ONR under Grant N00014-19-1-2100.]