Abstract
This paper investigates the bifurcations of the periodic solutions in the piecewise linear systems. Firstly the equation about amplitude-frequency response is deduced by the averaging method. Then the bifurcation classification is conducted by applying the singularity theory. The effects of the two parameters, the mass and the excitation amplitude, are discussed. The balance position will be changed when the quality changed, So the system is divided into two kinds of state. The results show that the parameter plane is divided into thirteen regions where bifurcation types are different. At last, discussing the amplitude- frequency response of different regions. this paper provides some theoretical guidance for system of considering load variation, and it is significant to help research the change in amplitude-frequency characteristic of piecewise linear system.
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