Nonlinear vibration modeling and analysis of bolted thin plate based on non-uniformly distributed complex spring elements

Due to the existence of bolt influence zone, the interface pressure of bolted joint presents a nonuniform distribution. The nonlinear mechanical behaviors of variable stiffness and variable damping will also occur in bolted joints under varying degrees of forced vibration. In this paper, a nonlinear finite element analysis model of bolted thin plate is established by introducing displacement-dependent nonlinear complex spring elements with non-uniformly distributed parameters. Sinusoidal, parabolic and linearly distributed complex spring elements are used to simulate the non-uniform pressure distribution in the bolt influence zone, respectively. The stiffness and damping displacement-dependent parameters of the complex spring elements are described by higher-order polynomials, and a method to obtain the above parameters by inverse identification is proposed. In the case study, the non-linear finite element model created is used to calculate the resonance frequency and frequency domain response of bolted thin plate under five excitation levels. The maximum differences between the results and the measured values are 2.7% and 0.66%, respectively. The simulation results also reproduce the soft nonlinear vibration phenomenon of the bolted thin plate. Furthermore, by comparing the vibration analysis results of the linear model and nonlinear model for bolted thin plate, the reason for the soft nonlinear phenomenon produced is explained.