• Parallel magnetic–piezoelectric NESs with two repulsive magnets are proposed. • A novel quantitative criterion is proposed to identify NES-induced SMRs. • A response-regime-based framework enables systematic NES parameter optimization. • Proposed parallel NESs outperform a benchmark single NES across regimes. • The proposed model, methodology and prototype are validated experimentally. The nonlinear energy sink (NES) has attracted increasing attention in vibration suppression and energy harvesting (VSAEH) due to its targeted energy transfer (TET) capability. The performances of NES-equipped structures, however, are highly sensitive to NES-induced response regimes—periodic, quasi-periodic, and strong modulated responses (SMRs). Despite this, quantitative SMR identification and regime-guided NES design methodologies remain underdeveloped. Moreover, multi-degree-of-freedom (MDOF) NESs, which are expected to provide richer energy dissipation pathways and enhanced harvesting potential compared with single-DOF designs, have received limited investigation for integrated VSAEH. To address these challenges, this study develops tunable parallel magnetic-piezoelectric NESs incorporating dual repulsive magnets (P-2RMPNESs) and establishes their coupled dynamic model with the primary structure. A novel SMR identification criterion is proposed and embedded into an optimization framework, enabling response-regime-based parametric optimization of both P-2RMPNESs and a benchmark single 2RMPNES. Simulation results show that the single 2RMPNES achieves effective VSAEH only under SMRs, whereas the P-2RMPNESs demonstrate excellent performance under quasi-periodic and periodic responses, and exhibit superior suppression under localized SMRs at high-amplitude excitations. The generalizability of the proposed SMR-based optimization framework is demonstrated via its extension to a tri-magnet configuration (3RMPNES), without modifying the optimization scheme. Experimental validation confirms the accuracy of the proposed model, criterion, and optimization method, demonstrating that the P-2RMPNESs outperform the 2RMPNES. Overall, this work establishes a response-classification-based framework for NES design and optimization, clarifies the link between NES-induced response regimes and system performances, and provides valuable guidance for developing multifunctional MDOF NESs that integrate VSAEH.
Guo et al. (Tue,) studied this question.