The domestic and international research methods for static and dynamic analyses of bolted joint structures were summarized. The research status, advantages and disadvantages of different numerical models and theoretical models from simple static analysis to complex nonlinear dynamic analysis were reviewed. Finally, it was pointed out that establishment of all-purpose models for structural analysis of bolted joints combining with engineering projects might become a hot research concentration in the future.

In this paper, an improved Fourier series method (IFSM) is employed to determine the transverse free vibration of a multi-span non-uniform shafting system with arbitrary boundary conditions. At first, the differential equation for the transverse free vibration of a uniform beam with lumped masses is formulated. Then, the mass and stiffness matrices for the shafting are derived using the IFSM, and then all the eigenvalues and eigenvectors are readily obtained by solving a standard matrix eigenvalue equation. In this method, the displacement function is expanded as a single Fourier cosine series plus an auxiliary polynomial function. The auxiliary function is used to overcome the discontinuities of the resilient boundary. Numerical results are presented to validate the correct of the method. And the stiffness effect of connecting flange is described.