Stability and Periodic Motions for a Non-Smooth Vibration Absorber Model with Limited Amplitude
In this paper,the stability and periodic motions for a limited vibration absorber model with the piecewise smooth property are studied.The dynamic model of a kind of limited vibration absorber is established.The existence of the admissible equilibrium point of the model is discussed,and the stability of the admissible equilibrium point is analyzed by Liénard-Chipart stability criterion.With the aid of pa-rameter transformations,the vibration absorber model with limited amplitude is transformed into a four-dimensional piecewise smooth system with two switching manifolds.By the first integrals of the system,the Melnikov function of the four-dimensional parametric piecewise smooth dynamic system under the condition that the unperturbed system has a family of periodic orbits is obtained.The existence and number of periodic orbits of the system under different parameter conditions are discussed,and the phase diagram configuration is given by numerical simulation method to verify the correctness of the theoretical results.The results show that different clearance parameters affect the number and relative positions of periodic orbits.
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