The vibration characteristics of bolted structures are crucially affected by the pre-tightening torque. An approach for identifying the pre-tightening torque dependent stiffness parameters of bolted joints is proposed in this paper. Firstly, the interface of the bolted joint is characterized by the thin layer element with the isotropic material property, and the parameter value of the property is assigned relative to the distance from the center of the bolt; the influence of the bolt is ignored. Secondly, the model updating method is adopted to identify the parameters of thin layer elements using experimental data, and modal data under different values of pre-tightening torque in the range of 2 N·m~22 N·m are obtained; the torque wrench is used to determine the pre-tightening torque in the modal test. Finally, after identifying the material parameters using partial experimental data on pre-tightening torque range, the empirical equation of the interface parameters with the pre-tightening torque parameter is obtained by curve fitting and the rest of the experimental data are used to verify the accuracy of the fitted empirical equations. It is concluded that this method can obtain all the parameters of the equivalent thin layer elements within a certain range of pre-tightening torque, which can provide a reference for the empirical modeling of bolted structures, improve modeling efficiency and reflect the characteristic performance of real structural dynamics.

A collision with clearance causes obvious nonlinearity in structures, and dynamic response analysis plays an important role in predicting the mechanical performance of the structure. The general form of the nonlinear dynamic equation of a structure and the clearance modeling method are introduced, and the clearance-caused nonlinear term is expressed by nonlinear impact forces. Different clearance collision models of local nonlinear structures are presented. The relationships between different impact forces and clearances are analyzed by two rigid sphere models. The solution methods of the nonlinear dynamic equation are compared by a vibro-impact response, such as the Newmark-β method combined with the Newton–Raphson method, generalized α method and precise integration method. The single degree of freedom model is adopted to compare the efficiency of the different numerical integration algorithms. Taking the beam structure model as a case study, the accurate nonlinear collision model with clearance is established by using the impact force model with high accuracy, and the accuracy of the model is verified by comparing the reference model with the numerical model.