Multistable Response Characteristics in Nonlinear Energy Sinks With Piecewise Linear Stiffness

Abstract

Abstract. This work examines the multistable response of a nonlinear energy sink (NES) incorporating piecewise linear stiffness. The introduction of piecewise linear stiffness modifies the system’s stiffness characteristics, broadens the resonance conditions, allows the existing damping elements to dissipate energy more efficiently, and limits the displacement of the nonlinear energy sink. The governing equations, derived from Newton’s second law, are solved using the incremental harmonic balance (IHB) method to compute the steady-state responses. Stability analysis reveals the coexistence of two periodic responses, two quasi-periodic oscillations, and chaotic states within these regions. The energy dissipation efficiency of the NES is evaluated, and the energy distribution across the different response types is analyzed; specifically, within the multistable response region in the frequency interval of 38.260–44.280 rad/s, the optimal response branch achieves nearly 100% maximum energy absorption, and the average energy absorption efficiency reaches 80%. Numerical simulations confirm the IHB results, showing excellent agreement in predicting the complex nonlinear dynamics.