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

This paper investigates the vibration suppression of an elastically supported nonlinear cantilever beam attached to an inertial nonlinear energy sink (NES). The nonlinear terms introduced by the NES are transferred as the external excitations acting on the beam. The governing equations of the nonlinear beam with an inertial NES are derived according to the Lagrange equations and the assumed mode method. The linear and nonlinear frequencies of the beam are numerically obtained by the Rayleigh-Ritz method and the direct iteration method, respectively. The frequencies are verified by the results of the finite element analysis and literature. The responses of the beam under shock excitations and harmonic excitations are numerically solved by the fourth-order Runge-Kutta method. The suppression effect of the inertial NES on the transverse vibration of the beam is evaluated through the values of amplitude reduction and energy dissipation. In addition, a parametric analysis of the inertial NES is conducted to improve the vibration reduction effect of the NES on the beam. © 2023 World Scientific Publishing Company.