Parameter optimization analysis of a nonlinear energy sink system under base harmonic excitation

In order to obtain the optimal stiffness parameter of a nonlinear energy sink (NES) system under base excitation, the complex-averaging method was employed to derive the equation of a corresponding slow dynamics system with 1:1 resonance. The corresponding necessary condition of the strongly modulate response (SMR) and analytical equation of the fixed point were also obtained. Sequently, the lower limit and upper limit were solved based on the characteristics and analytical equation of the fixed point respectively. The numerical simulation results indicate that the fixed point solved by the analytical equation of the fixed point is in agreement with the counterpart directly calculated using Runge-Kutta method. Moreover, the former is also approximate to the stable response of the original dynamic system. Additionally, the slow dynamics system is convenient for computation and has rational results. The optimal stiffness areas for NES system trend to be larger with the increase of damping parameters. Compared with TMD system, NES system has broader frequency band for vibration attenuation but it is of lower efficiency at frequencies close to the inherent frequency and is also easily affected by the excitation magnitude. © 2019, Editorial Office of Journal of Vibration and Shock. All right reserved.