The second order nonlinear longitudinal acousticsudin a cylindrical combustion chamber are studiedudfor the case of an unstable second mode. A modaludanalysis is undertaken and a continuation methodudis used to determine the limit cycle behavior of theudtime dependent amplitudes of the acoustic modesudas functions of the linear stability of the unstableudacoustic mode. It is shown that if an insufficientudnumber of modes are included in the truncated system,udbifurcations of the primary limit cycle occur.udThe energy in the limit cycles is analyzed and theudbifurcations are shown to occur as a means of increasingudthe amount of energy transfer out of theudunstable acoustic mode and into the stable acousticudmodes through the nonlinear terms.
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