Grounded Damping Bistable Nonlinear Energy Sink: Theoretical Modeling and Numerical Validation for Enhanced Broadband Vibration Suppression

Bistable nonlinear energy sinks (BNES) suffer from restricted activation of strongly modulated responses (SMR) due to excitation-amplitude sensitivity, limiting broadband vibration control. This study proposes a grounded damping bistable nonlinear energy sink (GD-BNES) to lower energy transfer thresholds by optimized damping configuration. Based on a two-degree-of-freedom coupled dynamical model, this study analytically investigates the topological evolution of slow invariant manifold (SIM) and bifurcation characteristics via the complexification-averaging method and multi-scale analysis. The triggering conditions for SMR are quantitatively identified. Numerical verification confirms that the GD-BNES exhibits enhanced efficiency at high energy levels under both harmonic and impact excitations compared to cubic NES (CNES) and BNES. This performance superiority stems from its unique independent dissipation pathway provided by grounded damping and expanded stability domain through negative stiffness effects. This finding has important practical significance for enhancing the vibration suppression efficacy and operational robustness of NES, while offering a new design paradigm for NES structural configurations.