To investigate the problem of vibration jumping in the aero-engine with squeeze film damper,the aero-engine rotor was simplified as a rigid-rotor with elastic-support.Dynamic equations of the system were established according to the oil-film force model,which were obtained by short bearing approximation and π-film assumption.The transition set of system was obtained by averaging method and Chen-Langford (C-L) method.The parametric plane of bearing coefficient and eccentricity coefficient was divided into three different regions by the transition set.Given different characteristics of bifurcation in each region,the region Ⅰ is an ideal region without jumping phenomenon.Then,an additional structure with "soft characteristic" of nonlinearity could expand the ideal region Ⅰ,decrease the jumping interval and broaden the range of optimization parameter selection.