The significant effect of the closed-detached response on the system is often ignored by traditional vibration control and energy-harvesting devices. In this study, we design a composite vibration energy-harvesting damper by combining the lever-type nonlinear energy sink, the three-spring quasi-zero stiffness structure, and the suspended magneto-electric energy harvester. The analytical as well as the numerical solutions are obtained using the harmonic balance method combined with the arc-length extension method as well as the Runge–Kutta method, respectively. Numerical solutions support analytical solutions. The presence of the closed-detached voltage makes composite system voltage harvesting more efficient. In addition, we investigate the performance of vibration control and energy harvesting by changing the dynamic parameters of the system such as attached mass, stiffness, and fulcrum position. Finally, when compared with the traditional absorber, the proposed absorber shows great improvement either in vibration control or in energy harvesting.
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