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In this paper, the periodic motion, bifurcation and chatter of two-degree-of-freedom vibratory system with dry friction and clearance were studied. Slip-stick motion and the impact of system motions were analyzed and numerical simulations were also carried out. The results showed that the system possesses rich dynamics characterized by periodic motion, stick-slip-impact motion, quasi-periodic motion and chaotic attractors, and the routs from periodic motions to chaos observed via Hof bifurcation or period-doubling bifurcation. Furthermore, it was found that there exists the chatter phenomena induced by dry friction in low frequency, and the windows of chaotic motion are broadened in the area of higher excitation frequencies as the dry friction increases.

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Abstract:The vibration transmissibility properties of a honeycomb paperboard are investigated by experiments. The analysis of the steady-state response of mass loaded honeycomb paperboard system to harmonic base excitation is presented in this paper. An experiment system is formulated and the vibration transmissibility data are obtained under different base excitation amplitude conditions. According to the transmissibility experiments data, we can assume that both the stiffness and damping properties are nonlinear. The hysteresis loops of the honeycomb paperboard-mass system are experimentally obtained, and are used to investigate the stiffness and damping properties of the system. The honeycomb paperboard's uni-directional vibration transmissibility behavior is modeled by using nonlinear stiffness, the combination of velocity proportional damping and quadratic type nonlinear damping components. The parameters in the model are identified by use of one-term harmonic balance method and the parameters under different load condition are presented. The model and the parameters in this paper can be used to simulate the transmissibility-frequency curves accurately. The model can be used for understanding the vibration transmissibility behaviors of the honeycomb paperboard, and the simulated transmissibility-frequency curves can be used for the packaging design.