Non-uniform Distributed Parameter Modeling Of Bolted Joints And Its Application In Vibration Analysis Of Bolted Plates

Whether it is aerospace,industrial production or daily life facilities,bolt connection is almost used in all these mechanical equipment.Compared with the whole structure,the stiffness weakening and damping effect of the bolted joint will affect the mechanical properties of the whole structure,so it is necessary to establish the bolted joint model efficiently and accurately and apply it to the static and dynamic analysis of the bolted joint structure.Under the bolt preload,the pressure at the interface of the bolt joint(that is,the bolt influence zone)has the characteristics of non-uniform distribution,which will lead to the non-uniform stiffness and damping at the interface of the bolt joint.Therefore,it is necessary to consider the influence of the non-uniform distribution of the pressure at the bolt joint on the dynamic characteristics of the bolt connection structure.In this paper,the model of bolted joint with non-uniform distribution of parameters is established and applied to bolted thin plate structure(1)For bolted thin plate structure,the stiffness and damping characteristics of bolted joint interface are simulated by complex spring element with non-uniform distribution of parameters.The stiffness and damping parameters of complex spring element are identified by backstepping identification technology based on genetic algorithm,and the linear finite element dynamic model of bolted thin plate structure is established.Through the case study,the natural characteristics and vibration response of the model are simulated,and the rationality of the model is verified by comparing with the corresponding experimental results.(2)Based on the linear finite element dynamic model of bolted thin plate structure,the nonlinear complex spring element with displacement dependence is introduced.The displacement dependent parameter expression of complex spring element is determined by backstepping identification technology and numerical fitting method,and the nonlinear finite element dynamic model of bolted thin plate structure is established.The nonlinear vibration response of the model is solved by Newton Raphson method,and the rationality of the analysis results is verified by experiments.Furthermore,based on the model,the reason of nonlinear vibration is explained from the vibration mechanism.(3)For the bolted thin plate structure,the mechanical properties of the overlapped part of the bolted thin plate structure are simulated by the virtual material with non-uniform distribution of parameters.The parameters of the storage modulus and energy consumption modulus of the virtual material are determined by the backstepping identification technology.The linear semi-analytical dynamic model of the bolted thin plate structure is established.In addition,the innovative formula for solving the frequency response function between any hammering point and pick-up point of the semi analytical model is given.Through the case study,the natural characteristics and vibration response of the model are simulated,and the rationality of the model is verified by comparing with the corresponding test results.(4)Based on the established linear semi-analytical dynamic model of bolted thin plate structure,the nonlinear virtual material parameters with displacement dependence are introduced.The displacement dependence expression of virtual material parameters is determined by backstepping identification technology and numerical fitting method,and the nonlinear semi-analytical dynamic model of bolted thin plate structure is established.The incremental harmonic balance method,which is suitable for this model,is proposed to solve the nonlinear vibration response iteratively.The results are verified by experiments,and the virtual material model is used to explain the nonlinear vibration of the connecting plate.The research results of this paper can provide a reference for the simplified modeling of bolted joints considering the non-uniform distribution of pressure and the study of linear and nonlinear vibration characteristics of the model,and further provide technical support for the engineering design and anti-vibration optimization of bolted structures.