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Abstract Numerous recent works have established the potential of various types of metamaterials for simultaneous vibration control and energy harvesting. In this paper, we investigate a weakly nonlinear metamaterial with electromechanical (EM) local resonators coupled to a resistance-inductance shunt circuit, a system with no previous examination in the literature. An analytical solution is developed for the system, using the perturbation method of multiple scales, and validated through direct numerical integration. The resulting linear and nonlinear band structures are used for parametric analysis of the system, focusing on the effect of resonator and shunt circuit parameters on band gap formation and vibration attenuation. This band structure analysis informs further study of the system through wavepacket excitation as well as spectro-spatial analysis. The voltage response of the system is studied through spatial profiles and spectrograms to observe the effects of shunt inductance, nonlinearity, and their interactions. Results describe the impact of adding a shunted inductor, including significant changes to the band structure; multiple methods of tuning band gaps and pass bands of the system; and changes to wave propagation and voltage response. The results demonstrate the flexibility of the proposed metamaterial and its potential for both vibration control and energy harvesting, specifically compared to a previously studied system with resistance-only shunt.
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A nonlinear analysis of a Duffing oscillator with a nonlinear electromagnetic vibration absorber–inerter for concurrent vibration mitigation and energy harvesting
Abstract Several investigators have taken advantage of electromagnetic shunt-tuned mass dampers to achieve concurrent vibration mitigation and energy harvesting. For nonlinear structures such as the Duffing oscillator, it has been shown that the novel nonlinear electromagnetic resonant shunt-tuned mass damper inerter (NERS-TMDI) can mitigate vibration and extract energy for a wider range of frequencies and forcing amplitudes when compared to competing technologies. However, nonlinear systems such as the NERS-TMDI are known to exhibit complex stability behavior, which can strongly influence their performance in simultaneous vibration control and energy harvesting. To address this problem, this paper conducts a global stability analysis of the novel NERS-TMDI using three approaches: the multi-parametric recursive continuationWe emphasize that these assume method, Floquet theory, and Lyapunov exponents. A comprehensive parametric analysis is also performed to evaluate the impact of key design parameters on the global stability of the system. The outcome indicates the existence of complex nonlinear behavior, such as detached resonance curves, and the transition of periodic stable solutions to chaotic solutions. Additionally, a parametric study demonstrates that the nonlinear stiffness has a minimal impact on the linear stability of the system but can significantly impact the nonlinear stability performance, while the transducer coefficient has an impact on the linear and nonlinear stability NERS-TMDI. Finally, the global sensitivity analysis is performed relative to system parameters to quantify the impact of uncertainty in system parameters on the dynamics. Overall, our findings show that simultaneous vibration control and energy harvesting come with a considerable instability trade-off that limits the range of operation of the NERS-TMDI.
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- Award ID(s):
- 1944032
- PAR ID:
- 10493229
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Nonlinear Dynamics
- Volume:
- 112
- Issue:
- 8
- ISSN:
- 0924-090X
- Format(s):
- Medium: X Size: p. 5847-5862
- Size(s):
- p. 5847-5862
- Sponsoring Org:
- National Science Foundation
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