Vibration suppression of an elastic beam with boundary inerter-enhanced nonlinear energy sinks

Nonlinear vibration absorbers have been widely used for vibration suppression of elastic structures, but they were usually placed within the structures. However, designing such a vibration damping device within an engineering structure is possibly difficult. In this paper, an inertial nonlinear energy sinks (NES) is mounted on the boundaries of the elastic beam to suppress its vibration. Although this vibration suppression approach is more in line with engineering requirements, it introduces nonlinear oscillators at boundaries. This brings certain difficulties to the structural vibration analysis and the optimal absorber design. An approximate analytical approach for the steady-state response is developed in this work and verified by numerical solutions. The comparison with the uncontrolled system demonstrates the high-efficiency vibration suppression of the inertial NES installed on the boundary. Besides, the optimization of the NES parameters is performed. Resonance amplitude of the elastic structure can be reduced by 98% with the optimized NES. In summary, this paper proposes a novel approach to suppress the bending vibration of elastic structures through boundary NESs. The vibration reduction effect is very significant, and it is more feasible to implement. Therefore, this work is helpful to study the vibration of elastic structures with nonlinear boundaries and to promote the application of nonlinear vibration absorbers. Graphic abstract A boundary damping strategy is proposed to solve the problem of the difficulty of installing the vibration absorber in engineering. Introduce an inertial nonlinear energy sinks (NES) to reduce the weight of the shock absorber. The nonlinear boundary is separated and merged into the elastic beam vibration control equation to realize the decoupling of the continuum model. Resonance peak of the elastic structure can be reduced by 98% with the optimized NES. This work is helpful to study the vibration of elastic structures with nonlinear boundaries and to promote the application of nonlinear vibration absorbers.