Nonlinear energy sink (NES) systems primarily dissipate energy through damping components, and the location of these components significantly influences system performance. However, the impact of grounded damping—particularly grounded nonlinear damping—on the vibration suppression performance of NES systems has not been sufficiently studied. In this paper, grounded linear damping and grounded cubic damping are introduced into a combined stiffness NES, where the stiffness consists of piecewise linear and cubic terms. This leads to a novel combined grounded damping NES. The complex dynamic characteristics of this 2-degree-of-freedom system are analyzed. Using the complexification-averaging method, an analytical solution for the system amplitude is derived. Based on the slow-flow equations, the influence of system parameters on the topological shape of the slow invariant manifold (SIM) is investigated. Furthermore, the vibration suppression performance of the optimized combined stiffness NES, grounded linear damping NES, grounded cubic damping NES, and combined grounded damping NES is evaluated under various harmonic and random excitations using the nutcracker optimization algorithm (NOA). The results show that introducing grounded linear and cubic damping into the combined stiffness NES effectively improves its vibration suppression performance. The proposed combined grounded damping NES also exhibits significant potential for vibration suppression under different types of excitation.
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