Transverse vibration suppression of an inclined beam with a nonlinear energy sink

Abstract

A large number of inclined beam structures suffer from vibration problems. In this paper, the transverse nonlinear vibration model of an inclined beam is established for the first time to study the influence of the inclination angle. Moreover, a nonlinear energy sink (NES) is introduced to control the forced vibration of the inclined beam. The nontrivial static equilibrium configuration caused by weight is solved. Furthermore, the governing equation of the inclined beam-NES system is derived around static configuration. The effects of the inclination angle on the natural frequencies are studied. Meanwhile, the nonlinear dynamic response of the coupled system is analyzed qualitatively and verified numerically. The results show that the decrease in the inclination angle tends to increase the natural frequencies. Moreover, the low-order natural frequency of the system is more sensitive to the influence of the inclination angle and cannot be ignored. In addition, the research shows that the inclination angle affects the parameter design of NES. However, suitable parameters of the NES can achieve superior damping efficiency for vibration control of inclined beams at different angles of inclination. Thus, this research proposes a novel model for inclined engineering structures and provides the necessary theoretical basis for designing NES to reduce vibration.