Multiple Rotary Nonlinear Energy Sinks for vibration control of flexible beams

Nonlinear Energy Sinks (NES) provide passive vibration mitigation through nonlinear coupling with a secondary mass, enabling broadband energy dissipation without the need for frequency tuning. Among existing configurations, the rotary nonlinear energy sink (RNES) is a rotating device that introduces a purely inertial, potential-free nonlinear coupling with the host structure. In this work, one to three RNES devices are attached to a simply supported Euler–Bernoulli beam to achieve multimodal passive vibration control. Reduced-order equations of motion are derived using an assumed-modes approach and employed for extensive numerical investigations. Reference RNES designs are obtained through a hybrid optimization procedure targeting balanced vibration suppression across the first three bending modes while maintaining lightweight and compact attachments. The results demonstrate that RNES devices can simultaneously mitigate multiple structural resonances, with control performance systematically improving as the number of devices increases, although positive coupling effects were observed mainly for the first resonance. For the three-RNES configuration, peak vibration reductions exceeding 80% are achieved at the reference resonances with a total added mass of only 1% of the beam mass. Detailed dynamic analyses reveal the emergence of complex rotational regimes, including modulated, quasi-periodic, and fully rotational motions. Nevertheless, effective vibration mitigation is consistently maintained over a broad range of excitation levels and initial conditions. The findings highlight the potential of multiple-inertia RNES configurations as a robust and broadband passive control strategy for flexible structures, with performance comparable to cubic NES and TMD devices, while maintaining a lightweight and compact design.