THE DIRECT AND INDIRECT POWER FLOWS OF THREE NON-CONSERVATIVELY SERIES COUPLED OSCILLATORS

Abstract

The formulae of power flows among three non-conservatively series coupled oscillators excited by random forces have been derived and analyzed. The analysis results show that the theory of the power flows of both three conservatively series coupled oscillators and two non-conservatively coupled oscillators are special examples of the theory of the power flows of three non-conservatively series coupled oscillators, and the reciprocity of the indirect power flows among three non-conservatively series coupled oscillators is untenable. The relationships between the power flows and the parameters of coupling have been studied by means of the numerical method. The numerical results show that the indirect power flows correspond to the resonant transmission between the indirectly coupled oscillators, and the indirect power flows should not be ignored in strong coupling conditions. Using the definition of the direct coupling loss factors (coupling loss factor in classical Statistical Energy Analysis) and the power flows of three non-conservatively series coupled oscillators, the influence of the indirectly coupled oscillators on the direct coupling loss factors has been studied by means of the numerical method. It is shown that the existence of the indirectly coupled oscillators has great influence on the direct coupling loss factors. The direct coupling loss factors in multi-coupled oscillator system are different from the coupling loss factors of the two coupled oscillators, and it is necessary to modify the direct coupling loss factors when the energy balance equations of SEA are modified. Experimental verification has been carried out with a floating raft isolation system. The agreement between the results estimated by SEA and those experimentally measured are good.