Two-modal resonance control with an encapsulated nonlinear energy sink

•A encapsulable nonlinear energy sink with viscous and elastic limit is proposed.•The piecewise nonlinear model is accurately fitted and approximately analytically solved.•A multi-objective optimization strategy to control multi-modal resonance is proposed.•The encapsulable nonlinear energy sink is proven to be able to suppress two-resonance modes. Nonlinear energy sink (NES) has received extensive attention as a broadband vibration control strategy. Generally, the vibration of the NES vibrator is unconstrained. Moreover, the vibration suppression is for a single modal resonance. In this paper, an encapsulated NES (E-NES) is proposed to control two resonance modes. Meanwhile, a strategy for optimizing two-resonance mode is also proposed. In practical applications, the vibration of the NES vibrator needs to be limited within a certain range. The vibration of the vibrator of the proposed E-NES is limited by a spring and a damping capacity with a gap. A dynamic model with non-smooth nonlinearity of a two-degree-of-freedom (two-DOF) system coupled with an E-NES is established. The non-smooth model is fitted by a hyperbolic tangent function. Then the continuous nonlinear model is analyzed approximately analytically and simulated numerically. The experimental platform is designed to verify the effectiveness of theoretical research. Moreover, the E-NES parameters are optimized by the differential evolution algorithm. The results show that the optimized design of the E-NES can achieve almost 90% suppression efficiency for both resonance peaks. On the whole, the proposed NES is a promising vibration control strategy due to its lower cost and high efficiency. Moreover, this NES can be accommodated in a box, which presents strong convenience in engineering.