Analysis of the dynamic characteristics of rod and beam structures with nonlinear stiffness boundaries

Nonlinear boundaries exist in many engineering structures and significantly influence the vibration of systems. The dynamic characteristics of a rod or beam structure with nonlinear stiffness boundaries were studied. The traveling wave method and the variable separation method were used to analyze the dynamic characteristics of the rod, and the relationship between the two approaches was investigated. For the beam, the incident propagating and nearfield waves were considered, respectively. The relationships between the dimensionless frequency, displacement, reflection coefficient, and phase were discussed by using the harmonic balance method. Finally, the backbone and frequency response curves of the rod and beam structures were obtained by using the phase closure principle and the variable separation method. In order to verify the accuracy and effectiveness of the theoretical calculations, a finite element numerical simulation was carried out for the rod and beam models. The results show that the theoretical solutions compare well with the numerical simulation results.