Theoretical and experimental analysis of vibration reduction for piecewise linear system by nonlinear energy sink

The vibration reduction of a piecewise linear system coupled with a nonlinear energy sink (NES) is studied. Piecewise stiffness can restrain the large vibration while the NES enhances the control effect. An experimental device of the piecewise system coupled with the NES is deigned, and the governing equation is established with Newton's second law. Parameters of the system are obtained based on the experimental data. Especially, the nonlinear stiffness and the damping of the NES are identified by the restoring-force surface method. For a better accuracy during the analytical processing, a hyperbolic tangent function is introduced to fit the piecewise restoring force, instead of the Taylor series expansion. Considering the strong nonlinearity of the NES, the steady-state response of the coupled system is analyzed by the harmonic balance method (HBM), including the stability analysis. The numerical simulation and the experimental study verify that the result obtained with the HBM has a good accuracy. Compared with the response of the piecewise system without the NES, the NES has a significant damping performance for the piecewise structure. The NES even can restrain the vibration of the main system to a small region, in which the auxiliary spring in the piecewise system does not work. Based on the detailed investigations on the cubic nonlinear stiffness, the damping, and the mass of the NES, the control performance is optimized. A fork-shaped phenomenon exists at the top of the response curve of the main structure under optimized parameters. The discussion suggests that, a better control performance can be obtained with the NES which consists of a small mass, a strong nonlinear stiffness, and a well-designed damping.