Simultaneous broadband vibration suppression and energy harvesting using a magnetically enhanced piecewise-linear nonlinear energy sink

Abstract

Nonlinear energy sinks (NESs) offer significant potential for simultaneous broadband vibration suppression (VS) and energy harvesting (EH) through the use of an essentially nonlinear spring (ENS). However, realizing an ENS with minimal energy dissipation remains challenging. A piecewise-linear spring (PLS) provides a structurally simple and physically interpretable means to approximate nonlinear stiffness with little added friction. Yet, NESs employing a PLS often require a relatively high initial energy threshold to trigger targeted energy transfer (TET), resulting in reduced performance under low-level excitation. Magnetic springs can introduce bi-stable characteristics that enable snap-through oscillations, thereby lowering the energy threshold. Existing studies, however, have focused primarily on ungrounded magnetic spring configurations, leaving the influence of a grounded magnetic spring (GMS) on NES’s performance largely unexplored. To address this gap, this research integrates a tunable GMS into a piecewise-linear NES (PLNES) to reduce the energy threshold, thereby facilitating TET activation and enhancing broadband VS and EH performance. Four interconnected studies are undertaken: 1. Magnetic Spring Modelling – A tunable multi-stable piezoelectric energy harvester (PEH) is developed by combining a cantilever beam with an adjustable magnetic assembly capable of achieving mono-, bi-, and tri-stable states. Two magnetic restoring force models, based on the magnetic single-point and two-point dipole approaches, are formulated and optimized via a multi-population genetic algorithm. Parametric sensitivity analyses are conducted for the optimal models. 2. Hybrid Multi-Stable Energy Harvesting – A multi-stable hybrid energy harvester (MSHEH), integrating a PEH and electromagnetic energy harvester (EMEH), is proposed and evaluated numerically and experimentally under various stability states. Optimal load resistances for balanced energy output across configurations are determined through optimization. 3. PLS Design Methodology – A systematic approach for designing a PLS is developed, enabling close emulation of a desired ENS using a cantilever beam constrained by single- or double-stop blocks. The designed PLSs are validated against the target ENS through both simulation and experiment. 4. Magnetically Enhanced PLNES (MPLNES) – A novel MPLNES is proposed by integrating a PLNES with a tunable GMS and a grounded EMEH. The GMS produces a position-dependent restoring force that shifts the NES’s equilibrium, enabling easier activation of large-amplitude oscillations. Numerical and experimental results confirm that the MPLNES triggers TET at lower excitation levels than the corresponding PLNES. A two-objective optimization reveals that the MPLNES achieves superior trade-offs between VS and EH, sustaining energy transfer over a wider range of excitation levels compared with the two other NES designs. Keywords Nonlinear energy sink; vibration suppression; energy harvesting; targeted energy transfer; essentially nonlinear spring; piecewise-linear spring; grounded magnetic spring; piezoelectric energy harvester; electromagnetic energy harvester; multi-stable dynamics.