The vibration control study of a coupling beam system attached to NESs

This study investigates the influence of nonlinear energy sinks (NESs) on the forced transverse vibration of a primary system, where the primary system is composed of two beams, boundary-supporting springs, internal supporting springs, and an elastic coupling element. The forced transverse vibration of the primary system with NESs is predicted by the Galerkin truncation method (GTM), where the reliability of the transverse vibration responses calculated by the GTM is verified by the harmonic balance method (HBM). On this basis, the influence of NESs on the forced transverse vibration of the primary system is investigated. Forced transverse vibration of the primary system with NESs is significantly influenced by the structural parameters of NESs, including their nonlinear stiffness, viscous damping, and motion mass. The complex dynamic behavior of the primary system with NESs appears in its forced transverse vibration. Under certain parameters of NESs, the targeted energy transfer phenomenon appears between the primary system and NESs. Furthermore, the influence of viscous damping of NESs on single-frequency responses of the primary system with NESs is monotonous, while the influence of nonlinear stiffness and motion mass of NESs on single-frequency responses of the primary system with NESs is nonmonotonic. A suitable combination of nonlinear stiffness and motion mass of NESs beneficially influences vibration reduction of the primary system.