In this paper, the bifurcations of resonance in an irrational system are studied. The system is derived from a linkage mechanism and its dynamic behavior is determined by smooth parameter . When , the nonlinear stiffness in the system is positive; when , it is negative; when , the system is linear. When increase from small to big, the system change from weakly nonlinear system to strongly nonlinear system. The research results show that the properties of irrational system are different from that of polynomial system. Finally we studied the evolution process of the resonance solution by employing singularity theory.
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