The (energy) loss factors in a dynamic system composed of a master dynamic system and an adjunct dynamic system that are coupled

Abstract

The (energy) loss factor (η) of a dynamic system is defined such that together with the stored energy (E) it yields the power Π dissipated in that dynamic system; (ωη)E=Π, where ω is the frequency and η, E, and Π are functions of ω. An externally driven master dynamic system is defined by the loss factor (η0) and the modal density (ν0). The relevant quantities in the absence of coupling are the external input power (Π0e), the stored energy (E00), and the power (Π00) dissipated. The conservation of energy demands Π0e=Π00. In the presence of coupling Π0e E00 and Π00 become the quantities Πe, E0, and Π0, respectively. The externally driven master dynamic system is coupled to an adjunct dynamic system defined by the loss factor (ηs) and the modal density (νs). The relevant additional quantities are the net power (Πs) transferred from the master dynamic system to the adjunct dynamic system and the stored energy (Es) and the power (Πs) dissipated in the adjunct dynamic system. The conservation of energy demands Πe=Π0+Πs. A number of (energy) loss factors may be defined to describe the energetics of these coupled dynamic systems. A few asymptotic relationships among these loss factors are cited. [Work supported by ONR.]