Statistical energy analysis of two spring-coupled oscillators

The response of two spring-coupled oscillators is investigated to develop our understanding of the weak coupling assumption in the modal approach to statistical energy analysis (SEA). The oscillators have stochastic uncoupled resonance frequencies that are normal distributed. For this case, the SEA coupling power proportionality holds for the ensemble average response, even for single frequency excitation, provided that a suitable definition of modal energy is adopted. It is seen that strength of coupling, from an ensemble point of view, is defined by the nondimensional ‘‘interaction strength.’’ This quantity may, for multi-modal systems, be interpreted as the ratio of the SEA conductivety to the product of the modal overlaps in each element, in which case the strength of the coupling measure agrees with the one that previously was found to govern the ensemble-averaged energies in one-dimensional wave guide systems.