Bolted joints are widely used for the mechanical assembly of engineering structures. It has been widely observed that fasteners turn loose when subjected to dynamic loads in the form of vibration or cyclic loading. Preload relaxation of threaded fasteners is the main factor that influences the joint failure under normal cyclic loading, but it is difficult to monitor the energy dissipation between the interface of the bolted joint. This paper presents an energy dissipation model for the bolted joint based on two-degree-of-freedom vibration differential mathematical model. A non-uniform pressure at the interface is considered and the resulted distinct stick-slip transitions along the contact interface are presented. The parameters of the model is calculated by using the fractal theory and differential operator method. Experiments are conducted to verify the efficiency of the proposed model. The results show that the theoretical mode shapes are in good agreement with the experimental mode shapes. According to the change of cyclic load and vibration frequency, the vibration response and the law of energy dissipation under different factors can be obtained. The results show that the vibration frequency and cyclic load are the main factors affecting the energy dissipation between interfaces. The energy dissipation of the contact surface of the bolted joints account for the main part of the energy dissipation of the bolted structure. As the preload increases, its energy dissipation decrease gradually. The results provide a theoretical basis for reducing micro-slip at the bolted joints interface.

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