Modelling and experimental validation of hysteresis loops in bolted joints

Frictional contact interfaces in bolted joints affect the overall structural dynamic properties and can be characterised using key features such as frequency response curves and hysteresis loops. Various hysteresis models, including LuGre, Valanis, and Bouc-Wen, have been employed to simulate the nonlinear behaviour in the tangential direction. In these models, the friction force is determined by solving a nonlinear differential equation numerically. Typically, obtaining an analytical solution for this equation is impractical, and no closed-form solution for the friction force is available, which causes difficulties in the identification of the model parameters using experimental results. In this paper, closed-form solutions for the friction force under general input is obtained and identified using both simulated and experimental results. An experimental test structure is designed, which allows pure excitation of the contact interface in the tangential direction of the joint contact interface. A 3-degree-of-freedom nonlinear reduced-order model is developed for the test structure, which is useful in joint contact interface characterisation. It is shown that at frequencies near the natural frequency, the relative displacement at the contact interface increases, leading to greater energy dissipation. Moreover, the accuracy of the base linear model- used as the foundation for developing the nonlinear reduced-order model- is crucial for reliably identifying the nonlinear parameters of the joint contact interface.