Vibration Reduction for an Asymmetric Elastically Supported Beam Coupled to an Inertial Nonlinear Energy Sink

Purpose  The present paper addresses the vibration reduction for an elastic beam with an asymmetric boundary condition that is clamped at one end and elastically supported at the other end. An inertial nonlinear energy sink (NES) is installed on the elastic support end to suppress the beam's vibration. Methods  The nonlinear terms introduced by the NES are transferred as the external excitations acting on the beam. The motion equations of the beam with an NES are derived according to Hamilton's principle and the Galerkin truncation method. The beam's natural frequencies and corresponding mode shapes are analytically obtained and verified with the results of the finite element method. The responses of the beam are numerically and analytically solved by the fourth order Runge–Kutta method and the harmonic balance method (HBM), respectively. Results  The good agreement among the results validates the present derivation of the theoretical model and numerical solutions. The steady-state responses of the beam with and without the NES are compared and analyzed in the time domain. Conclusions  The results demonstrate that adding the inertial enhanced NES can effectively reduce the resonance amplitude of the beam. Furthermore, a parametric optimization is conducted for NES to improve its performance. The results of this paper contribute to the application of NESs on the boundaries of elastic structures.