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Recently, dynamic analysis of a beam structure with nonlinear energy sink (NES) and various supports is attracting great attention. Most of the existing studies are about the beam structure with NES or nonlinear boundary supports with zero rotational restraint, respectively. However, there is little research accounting for such two types of complex factors simultaneously. In this work, the dynamic behavior of an axially loaded beam with both NES and general boundary supports is modeled and studied. The Galerkin truncated method (GTM) is employed to make the prediction of dynamic behavior of such a beam system, in which the mode functions of axially loaded Euler–Bernoulli beam with linear elastic boundary conditions are selected as the trail and weight functions. Then, the Galerkin condition is used to discretize the nonlinear governing equation of the beam system and establish the residual equations. The Runge–Kutta method is used to solve the residual matrix which consists of residual equations directly, and the harmonic balance method is also used to verify the results from the GTM. The influence of NES on vibration suppression and dynamic behavior of the beam structure is investigated and discussed. Results show that the vibration states of the beam structure can be transformed effectively through the change of NES parameters. On the other hand, the NES with suitable parameters has a beneficial effect on the vibration suppression at both ends of the beam structure.

The high-speed train speed has a higher requirement for stability and operating safety with its operating speed increasing. The main focus of this paper is on the fault characteristics analysis of a high-speed train transmission system. The governing equation and boundary conditions of the transmission system are derived using the finite element method, in which a Timoshenko beam element is introduced to represent the wheelset shaft, and a rigid mass element is utilized to represent the gears, bearings, and wheels. To investigate the vibration response mechanism of a high-speed train transmission system, the critical speed of the system and its modal response are given. According to the types of high-speed train component fault features, the local fault features of gear, bearing, and wheelset are given. Healthy and faulty systems with localized faults in gear, bearing, and wheelset are studied. The characteristics of amplitude and frequency are verified numerically and the transmission characteristics of signal and relation are explained when there is local fault defect in the system. The results show that under different fault types, the time domain response of the system has obvious periodic impulse response faults, and the fault frequency band characteristic distribution is different in the frequency domain response. The simulation results are consistent with the experimental results.