Non-linear dynamic response of a beam with bolted joint based on modal shape transfer

The forced vibration of a beam with one end clamped and the other end bolted was studied. The nonlinear force-displacement characteristics of a bolted joint modeled using Iwan model were used to study the effect of nonlinearities in the bolted joint on the dynamic response of the beam based on the modal shape transfer principle. The modal shape transfer between different modal shapes caused by the hysteretic boundary condition was treated adopting the relative modal shape transfer method. The effects of the coupling between modes, the number of Jenkin's elements in Iwan model, the amplitude of the external excitation force, the modal damping and the stiffness of the bolted joint on the response of the beam's end were discussed with the frequency-amplitude response of the beam's end. It was shown that the new approach has a good convergence when dealing with the vibration problem of a continuous system with hysteretic boundary condition, the effect of the nonlinearity on the dynamic response of the beam system is finite, one-period motion and weak frequency-shift are revealed in a specified frequency-sweeping range, and the level of frequency-shift is sensitive to the stiffness of the bolted joint.