Vibration suppression and dynamic behavior analysis of an axially loaded beam with NES and nonlinear elastic supports

Abstract

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.