Some simple models describing the transition from weak to strong coupling in statistical energy analysis

Abstract

Two simple situations are considered of N mutually coupled oscillators excited at resonance by external random sources. Formulas are derived for oscillator energies that display explicitly the transition from weak to strong coupling between the oscillators. Average oscillator energy E, the average uncoupled oscillator energy Eu, and the coupled energy Ec are defined. In one situation, E, Eu, and Ec are equal; in the second situation, E is bounded by Eu and Ec.