# Dynamic Analysis of Bolted Cantilever Beam with Finite Element Method Considering Thread Relation
## 1 Introduction
Based on the theory of continuous Iwan model and beam element, [PERSON] [27; 28] skillfully transformed the solution of Iwan model parameters into the calculation of transverse and torsional displacement in Rayleigh damping by using neural network algorithm. The Rayleigh damping parameters of bolted structures were identified by three-layer neural network algorithm, and the dynamic response is verified, which shows the effectiveness of the method. [PERSON] [29] investigated a three legged structure with bolt connection. Jenkins element was used to model in transverse and torsional directions at the joint, and the degrees of freedom in other directions were simplified as linear springs. The comparison of the response of the structure under different frequencies with that of the simplified model proved the effectiveness of the simplified model. [PERSON] [30] scrutinized Iwan model to simulate the tangential hysteretic characteristics of the joint surface and used the model to simplify the model. The validity of the model was verified by response transfer experiment and response analysis. [PERSON] [31] created a three-dimensional finite element model in the ABAQUS to simulate the bolted joint under axial excitation, and studied the frictional stress, slip amplitude, and frictional work per unit area along two specified paths on the first thread. It was found that the finite elementresults agree with the experimental observations superbly. The Iwan model, however, was not extensively adopted owing to the high computational expense in a numerical simulation. [PERSON] [32] formulated a new experimentally validated expression for the bearing friction torque component in threaded joints with spherical and conical contact geometry, by extending two-dimensional Motosh model for various scenarios of contact pressure. In order to improve the understanding and the development of pertinent models, [PERSON] [33] designed a dynamic test bed, based on a bolted structure, and performed modal testing. The results of the experimental campaign showed the variation of the dissipation in a bolted joint and its apparent stiffness was a function of joint conditions. [PERSON] [34] investigated the FE bolted joints model updating of a hybrid metal/composite structure and proposed a new approach called \"doubly connective layer\" for hybrid interfaces. The updated model compared to the initial model simulates experimental results more appropriately. [PERSON] [35] discussed the dynamic characteristics of plastic plates with bolted joints and investigated the effects of tightening torque on the modal properties of the plates. By comparing the experimental and the numerical results, a modeling strategy for the boundary conditions between the plates was introduced and its validity was verified. On the basis of literature, most researchers mainly focus on the local nonlinearity caused by the nonlinear spring derived from the nonlinear bolt connection model. The stable and unstable bifurcation phenomena of nonlinear systems with local and nonlocal nonlinearities are studied. In addition, in the previous work, most researchers used the Euler Bernoulli model assumption to simplify the lateral vibration of bolted structures. This theory ignores the influence of shear deformation and moment of inertia on the dynamic response of bolted structures. Therefore, based on Timoshenko beam theory and finite element method, this paper introduces the model of screw connection and analyzes the dynamic response under different excitation. The results show that due to the local nonlinearity of the bolt, the whole bolt cantilever beam presents the characteristics of hardening type. In addition, the frequency response curve also displays the typical nonlinear phenomenon of instability and uncertainty, namely bifurcation, which preliminarily verifies the correctness and accuracy of the bolt cantilever beam model.