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Dual functionality of vibration attenuation and energy harvesting: effect of gradation on non-linear multi-resonator metastructures

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Abstract

Metastructures and phononic crystals could have several unique physical properties, such as effective negative parameters, tunable band gaps, negative refraction, and so on, which allow them to improve multi-physical performances at the materials level. Motivated by the elastic negative mass metastructures, this work reports the enhancement of bandwidth and vibration suppression while achieving better energy harvesting via non-linear attachments. We propose to consider the effect of spring softening and spring hardening simultaneously along with exploiting the coupled influence of multiple variables, such as spring stiffness, dam**, number of unit cells, electro-mechanical coupling coefficient and masses. A mathematical model of the metastructure having linear spring with nonlinear attachments is developed and analyzed numerically including the effect of functional gradation. Dimensionless parametric study is performed to tune two-cell and multi-cell models to enhance vibration suppression and energy harvesting performances. In an eight-cell model, the non-linear characteristic parameter is functionally graded from softening to hardening using exponential and power law to explore the dual functionality further. It is revealed that the resonant peak can be reduced by non-linear softening characteristics. For enhanced energy harvesting, a smaller value of mass ratio is preferred, while a larger value of dam** characteristic is suitable for vibration suppression. Under certain configurations, band structure of the phononic metastructure is capable of achieving absolute band gaps, resulting in frequency ranges, where waves cannot propagate. The comprehensive analysis presented here on the effect of various system parameters would lead to the design of non-linear multi-resonator metamaterials for the dual functionality of vibration attenuation and energy harvesting that can be applied in a wide range of automated systems and self-powered devices including the capabilities of real-time monitoring and active behaviour.

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References

  1. X.-K. Ge, Q.-X. Zhao, H. Shao, Y. Lu, Research on slenderness structure vibration induced by detouring flow symmetry breaking-taking the accident of tacoma narrow bridge damage caused by wind vibration as an example. J. Disaster Prevent. Mitig. Eng. 31(4), 430–435 (2011)

    Google Scholar 

  2. A.A. Zadpoor, Mechanical meta-materials. Mater. Horizon 3, 371–381 (2016)

    Google Scholar 

  3. T. Mukhopadhyay, S. Adhikari, Stochastic mechanics of metamaterials. Compos. Struct. 162, 85–97 (2017)

    Google Scholar 

  4. T. Mukhopadhyay, S. Adhikari, A. Batou, Frequency domain homogenization for the viscoelastic properties of spatially correlated quasi-periodic lattices. Int. J. Mech. Sci. 150, 784–806 (2019)

    Google Scholar 

  5. T. Mukhopadhyay, J. Ma, H. Feng, D. Hou, J.M. Gattas, Y. Chen, Z. You, Programmable stiffness and shape modulation in origami materials: emergence of a distant actuation feature. Appl. Mater. Today 19, 100537 (2020)

    Google Scholar 

  6. H. Wang, D. Zhao, Y. **, M. Wang, T. Mukhopadhyay, Z. You, Modulation of multi-directional auxeticity in hybrid origami metamaterials. Appl. Mater. Today 20, 100715 (2020)

    Google Scholar 

  7. T. Mukhopadhyay, S. Naskar, S. Adhikari, Anisotropy tailoring in geometrically isotropic multi-material lattices. Extreme Mech. Lett. 40, 100934 (2020)

    Google Scholar 

  8. S. Ghuku, T. Mukhopadhyay, Anti-curvature honeycomb lattices for mode-dependent enhancement of nonlinear elastic properties under large deformation. Int. J. Non-Linear Mech. 140, 103 (2022)

    Google Scholar 

  9. T. Mukhopadhyay, D. Kundu, Mixed-mode multidirectional poisson’s ratio modulation in auxetic 3d lattice metamaterials. Adv. Eng. Mater. 20, 2101183 (2021). https://doi.org/10.1002/adem.202101183

    Article  Google Scholar 

  10. H.H.C.T. Huang, G.L. Sun, Huang, On the negative effective mass density in acoustic metamaterials. Int. J. Eng. Sci. 47(4), 610–617 (2009)

    Google Scholar 

  11. H.H. Huang, C.T. Sun, Anomalous wave propagation in a one-dimensional acoustic metamaterial having simultaneously negative mass density and young’s modulus. J. Acoust. Soc. Am. 132, 2887–2895 (2012)

    ADS  Google Scholar 

  12. L. Jensen, C.T. Chan, Double-negative acoustic metamaterial. Phys. Rev. 70, 055602 (2004)

    Google Scholar 

  13. Y. Cheng, J.Y. Xu, X.J. Liu, One-dimensional structured ultrasonic metamaterials with simultaneously negative dynamic density and modulus. Phys. Rev. B 77, 045134 (2008)

    ADS  Google Scholar 

  14. Z. Yang, J. Mei, M. Yang, N.H. Chan, P. Sheng, Double-negative acoustic metamaterial. Phys. Rev. 101, 204301 (2008)

    ADS  Google Scholar 

  15. S. Adhikari, T. Mukhopadhyay, A. Shaw, N. Lavery, Apparent negative values of young’s moduli of lattice materials under dynamic conditions. Int. J. Eng. Sci. 150, 103231 (2020)

    MathSciNet  MATH  Google Scholar 

  16. T. Mukhopadhyay, S. Adhikari, A. Alu, Theoretical limits for negative elastic moduli in subacoustic lattice materials. Phys. Rev. B 99, 094108 (2019)

    ADS  Google Scholar 

  17. T. Mukhopadhyay, S. Adhikari, A. Alu, Probing the frequency-dependent elastic moduli of lattice materials. Acta Mater. 165, 654–665 (2019)

    ADS  Google Scholar 

  18. S. Adhikari, T. Mukhopadhyay, X. Liu, Broadband dynamic elastic moduli of honeycomb lattice materials: A generalized analytical approach. Mech. Mater. 157, 103796 (2021)

    Google Scholar 

  19. M. Reynolds, S. Daley, Enhancing the band gap of an active metamaterial. J. Vib. Control 23(11), 1782–1791 (2017)

    Google Scholar 

  20. L. Tang, Y. Yang, A multiple-degree-of-freedom piezoelectric energy harvesting model. J. Intell. Mater. Syst. Struct. 23, 1631–1647 (2012)

    Google Scholar 

  21. H.H. Huang, C.T. Sun, Wave attenuation mechanism in an acoustic metamaterial with negative effective mass density. New J. Phys. 11, 013003 (2009)

    ADS  Google Scholar 

  22. M.I. Hussein, M.J. Leamy, M. Ruzzene, Dynamics of phononic materials and structures: Historical origins, recent progress, and future outlook. Appl. Mech. Rev. 66, 013003 (2014)

    Google Scholar 

  23. A.F. Vakakis, O.V. Gendelman, L.A. Bergman, D.M. McFarland, G. Kerschen, Y.S. Lee, Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems, vol 156, (Springer Science & Business Media, Berlin, 2008)

  24. P. Malaji, M. Rajarathinam, V. Jaiswal, S. Ali, I. Howard, Energy Harvesting from Dynamic Vibration Pendulum Absorber, Recent Advances in Structural Engineering, vol 2, (Springer, Berlin, 2019) pp. 467–478

  25. A. Banerjee, E.P. Calius, R. Das, Reversible hysteresis for broadband magnetopiezoelastic energy harvesting. Appl. Phys. Lett. 95, 174103 (2009)

    Google Scholar 

  26. H.G.F. Cottone, L. Vocca, Nonlinear energy harvesting. Phys. Rev. Lett. 102, 080601 (2009)

    ADS  Google Scholar 

  27. Y. **a, M. Ruzzene, A. Erturk, Dramatic bandwidth enhancement in nonlinear metastructures via bistable attachments. Appl. Phys. Lett. 114, 093501 (2019)

    ADS  Google Scholar 

  28. B.S. Lazarov, J.S. Jensen, Low-frequency band gaps in chains with attached non-linear oscillators. Int. J. Non-Linear Mech. 42(10), 1186–1193 (2007)

    ADS  Google Scholar 

  29. Y. **a, M. Ruzzene, A. Erturk, Bistable attachments for wideband nonlinear vibration attenuation in a metamaterial beam. Nonlinear Dyn. 102, 1285–1296 (2020)

    Google Scholar 

  30. A. Banerjee, E.P. Calius, R. Das, The effects of cubic stiffness nonlinearity on the attenuation bandwidth of 1d elasto-dynamic metamaterials. Am. Soc. Mech. Eng. 2016, 50671 (2016)

    Google Scholar 

  31. G. Chakraborty, A. Mallik, Dynamics of a weakly non-linear periodic chain. Int. J. Non-Linear Mech. 36(2), 375–389 (2001)

    MATH  Google Scholar 

  32. D. Guyomar, A. Badel, E. Lefeuvre, C. Richard, Toward energy harvesting using active materials and conversion improvement by nonlinear processing. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(4), 584–595 (2005)

  33. T. Yang, S. Zhou, S. Fang, W. Qin, D.J. Inman, Nonlinear vibration energy harvesting and vibration suppression technologies: designs, analysis, and applications. Appl. Phys. Rev. 8(3), 031317 (2021)

    ADS  Google Scholar 

  34. Z. Chen, B. Guo, Y. Yang, C. Cheng, Metamaterials-based enhanced energy harvesting: a review. Phys. B 438, 1–8 (2014)

    ADS  Google Scholar 

  35. T. Yang, Q. Cao, Z. Hao, A novel nonlinear mechanical oscillator and its application in vibration isolation and energy harvesting. Mech. Syst. Signal Process 155, 107636 (2021)

    Google Scholar 

  36. A. Singh, T. Mukhopadhyay, S. Adhikari, B. Bhattacharya, Voltage-dependent modulation of elastic moduli in lattice metamaterials: emergence of a programmable state-transition capability. Int. J. Solids Struct. 208–209, 31–48 (2021)

    Google Scholar 

  37. A. Singh, T. Mukhopadhyay, S. Adhikari, B. Bhattacharya, Active multi-physical modulation of poisson’s ratios in composite piezoelectric lattices: on-demand sign reversal. Compos. Struct. 280, 114857 (2022)

    Google Scholar 

  38. B.B.D. Moura, M.R. Machado, T. Mukhopadhyay, S. Dey, Dynamic and wave propagation analysis of periodic smart beams coupled with resonant shunt circuits: passive property modulation. Eur. Phys. J. Spec. Top. 2021, 8 (2022)

    Google Scholar 

  39. M. Carrara, M.R. Cacan, J. Toussaint, M.E.M. Leamy, A. Jand-Ruzzene, Metamaterial-inspired structures and concepts for elastoacoustic wave energy harvesting. Smart Mater. Struct. 22, 065004 (2013)

    ADS  Google Scholar 

  40. Y. Li, E. Baker, T. Reissman, C. Sun, W.K. Liu, Design of mechanical metamaterials for simultaneous vibration isolation and energy harvesting. Appl. Phys. Lett. 111(25), 251903 (2017)

    ADS  Google Scholar 

  41. S. Kumar, N. Naidu, K. Banerjee, T.V.S.R.P. Anil-Babu, A review on metamaterials for device applications. Crystals 11, 518 (2021)

    Google Scholar 

  42. H.A. Sodano, D.J. Inman, G. Park, A review of power harvesting from vibration using piezoelectric materials. Shock Vibr. Digest 36, 197–206 (2004)

    Google Scholar 

  43. L. Tang, Y. Yang, A multiple-degree-of-freedom piezoelectric energy harvesting model. J. Intell. Mater. Syst. Struct. 23, 1631–1647 (2012)

    Google Scholar 

  44. A. Erturk, J. Hoffmann, D.J. Inman, A piezomagnetoelastic structure for broadband vibration energy harvesting. Appl. Phys. Lett. 94, 254102 (2009)

    ADS  Google Scholar 

  45. G. Hu, L. Tang, R. Das, Internally coupled metamaterial beam for simultaneous vibration suppression and low frequency energy harvesting. J. Appl. Phys. 123(5), 055107 (2018)

    ADS  Google Scholar 

  46. M. Rezaei, R. Talebitooti, W.-H. Liao, Exploiting bi-stable magneto-piezoelastic absorber for simultaneous energy harvesting and vibration mitigation. Int. J. Mech. Sci. 207, 106618 (2021)

    Google Scholar 

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Acknowledgements

TM would like to acknowledge the financial support from Science and Engineering Research Board (Grant no. SRG/2020/001398). PVM acknowledges Vison Group on Science and Technology (Grant no. KSTePS/VGST-K-FIST L2/2078-L9 / GRD No.765).

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Authors and Affiliations

  1. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, India

    A. Chaurha & T. Mukhopadhyay

  2. Vibration, Energy Harvesting and IoT Lab, BLDEA’s V. P. Dr. P. G. Halakatti College of Engineering and Technology, Vijayapur, India

    P. V. Malaji

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  1. A. Chaurha
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Correspondence to T. Mukhopadhyay.

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Chaurha, A., Malaji, P.V. & Mukhopadhyay, T. Dual functionality of vibration attenuation and energy harvesting: effect of gradation on non-linear multi-resonator metastructures. Eur. Phys. J. Spec. Top. 231, 1403–1413 (2022). https://doi.org/10.1140/epjs/s11734-022-00506-9

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