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Diode behaviors of curved elastic wave metamaterials with a nonlinear granular chain

具有非线性颗粒链的弯曲弹性波超材料中的二极管行为

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Abstract

This work studies about the band gap characteristics and nonreciprocal propagation of nonlinear elastic wave metamaterials which are composed of the curved particle chain with diatomic lattice. The incremental harmonic balance (IHB) method is applied to derive the nonlinear wave equation with fractional terms. Different curved angles and amplitude ratios are considered to show band gaps of nonlinear elastic waves. Both numerical calculations by the Runge-Kutta method and experiments are performed to support band gaps and diode behaviors. This study provides a new application of nonlinear phononic crystals and mechanical metamaterials with different curved directions.

摘要

本文研究了非线性弹性波超材料的带隙和非互易传播特性, 该结构由双振子弯曲颗粒链组成. 采用增量谐波**衡方法推导了具有分数项的非线性波方程. 考虑了不同的弯曲角度和振幅比对非线性弹性波带隙的影响. 通过Runge-Kutta方法数值计算和实验研究证实了超材料的带隙和二极管行为. 本研究为非线性声子晶体和具有不同弯曲方向的力学超材料提供了新的应用.

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References

  1. T. Wang, M. Sheng, and Q. Qin, Sound transmission loss through metamaterial plate with lateral local resonators in the presence of external mean flow, J. Acoust. Soc. Am. 141, 1161 (2017).

    Article  Google Scholar 

  2. S. Yves, and A. Alù, Extreme anisotropy and dispersion engineering in locally resonant acoustic metamaterials, J. Acoust. Soc. Am. 150, 2040 (2021).

    Article  Google Scholar 

  3. Z. Lv, P. Liu, Y. Ding, H. Li, and Y. Pei, Implementing fractional Fourier transform and solving partial differential equations using acoustic computational metamaterials in space domain, Acta Mech. Sin. 37, 1371 (2021).

    Article  MathSciNet  Google Scholar 

  4. K. Zhang, F. Hong, J. Luo, and Z. Deng, Topological edge state analysis of hexagonal phononic crystals, Acta Mech. Sin. 38, 421455 (2022).

    Article  Google Scholar 

  5. L. Tang, and L. Cheng, Periodic plates with tunneled Acoustic-Black-Holes for directional band gap generation, Mech. Syst. Signal Process. 133, 106257 (2019).

    Article  Google Scholar 

  6. X. Fang, J. Lou, Y. M. Chen, J. Wang, M. Xu, and K. C. Chuang, Broadband Rayleigh wave attenuation utilizing an inertant seismic metamaterial, Int. J. Mech. Sci. 247, 108182 (2023).

    Article  Google Scholar 

  7. C. Cai, J. Zhou, K. Wang, Q. Lin, D. Xu, and G. Wen, Quasi-zero-stiffness metamaterial pipe for low-frequency wave attenuation, Eng. Struct. 279, 115580 (2023).

    Article  Google Scholar 

  8. H. Xue, D. Jia, Y. Ge, Y. Guan, Q. Wang, S. Yuan, H. Sun, Y. D. Chong, and B. Zhang, Observation of dislocation-induced topological modes in a three-dimensional acoustic topological insulator, Phys. Rev. Lett. 127, 214301 (2021).

    Article  Google Scholar 

  9. B. **a, J. Zhang, L. Tong, S. Zheng, and X. Man, Topologically valley-polarized edge states in elastic phononic plates yielded by lattice defects, Int. J. Solids Struct. 239–240, 111413 (2022).

    Article  Google Scholar 

  10. K. Liang, J. He, Z. Jia, and X. Zhang, Topology optimization of magnetorheological smart materials included PnCs for tunable wide bandgap design, Acta Mech. Sin. 38, 421525 (2022).

    Article  MathSciNet  Google Scholar 

  11. H. Liu, W. Y. Tsui, A. Wahab, and X. Wang, Three-dimensional elastic scattering coefficients and enhancement of the elastic near cloaking, J. Elast. 143, 111 (2021).

    Article  MathSciNet  MATH  Google Scholar 

  12. W. J. Zhou, X. P. Li, Y. S. Wang, W. Q. Chen, and G. L. Huang, Spectro-spatial analysis of wave packet propagation in nonlinear acoustic metamaterials, J. Sound Vib. 413, 250 (2018).

    Article  Google Scholar 

  13. X. Fang, P. Sheng, J. Wen, W. Chen, and L. Cheng, A nonlinear metamaterial plate for suppressing vibration and sound radiation, Int. J. Mech. Sci. 228, 107473 (2022).

    Article  Google Scholar 

  14. V. F. Nesterenko, Dynamics of Heterogeneous Materials (Springer-Verlag, New York, 2001).

    Book  Google Scholar 

  15. V. F. Nesterenko, Propagation of nonlinear compression pulses in granular media, J. Appl. Mech. Tech. Phys. 24, 733 (1983).

    Article  Google Scholar 

  16. A. N. Lazaridi, and V. F. Nesterenko, Observation of a new type of solitary waves in a one-dimensional granular medium, J. Appl. Mech. Tech. Phys. 26, 405 (1985).

    Article  Google Scholar 

  17. V. F. Nesterenko, A. N. Lazaridi, and E. B. Sibiryakov, The decay of soliton at the contact of two “acoustic vacuums”, J. Appl. Mech. Tech. Phys. 36, 166 (1995).

    Article  Google Scholar 

  18. Y. Y. Yang, S. W. Liu, Q. Yang, Z. B. Zhang, W. S. Duan, and L. Yang, Solitary waves propagation described by Korteweg-de Vries equation in the granular chain with initial prestress, AIP Adv. 6, 075317 (2016).

    Article  Google Scholar 

  19. A. Kekić, and R. A. Van Gorder, Wave propagation across interfaces induced by different interaction exponents in ordered and disordered Hertz-like granular chains, Physica D-Nonlinear Phenomena 384–385, 18 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  20. Y. Starosvetsky, and A. F. Vakakis, Traveling waves and localized modes in one-dimensional homogeneous granular chains with no precompression, Phys. Rev. E 82, 026603 (2010).

    Article  MathSciNet  Google Scholar 

  21. K. R. Jayaprakash, A. F. Vakakis, and Y. Starosvetsky, Strongly nonlinear traveling waves in granular dimer chains, Mech. Syst. Signal Process. 39, 91 (2013).

    Article  Google Scholar 

  22. L. Bonanomi, G. Theocharis, and C. Daraio, Wave propagation in granular chains with local resonances, Phys. Rev. E 91, 033208 (2015).

    Article  Google Scholar 

  23. L. Liu, G. James, P. Kevrekidis, and A. Vainchtein, Strongly nonlinear waves in locally resonant granular chains, Nonlinearity 29, 3496 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  24. K. Vorotnikov, Y. Starosvetsky, G. Theocharis, and P. G. Kevrekidis, Wave propagation in a strongly nonlinear locally resonant granular crystal, Physica D-Nonlinear Phenomena 365, 27 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  25. C. Liu, Z. Du, Z. Sun, H. Gao, and X. Guo, Frequency-preserved acoustic diode model with high forward-power-transmission rate, Phys. Rev. Appl. 3, 064014 (2015).

    Article  Google Scholar 

  26. C. Fu, J. Xu, T. Zhao, and C. Q. Chen, A mechanical wave switch with tunable frequency output, Appl. Phys. Lett. 115, 191902 (2019).

    Article  Google Scholar 

  27. Y. Zhao, X. Zhou, and G. Huang, Non-reciprocal Rayleigh waves in elastic gyroscopic medium, J. Mech. Phys. Solids 143, 104065 (2020).

    Article  MathSciNet  Google Scholar 

  28. Y. Huang, and X. Zhou, Non-reciprocal sound transmission in electro-acoustic systems with time-modulated circuits, Acta Mech. Solid Sin. 35, 940 (2022).

    Article  Google Scholar 

  29. Z. N. Li, Y. Z. Wang, and Y. S. Wang, Tunable nonreciprocal transmission in nonlinear elastic wave metamaterial by initial stresses, Int. J. Solids Struct. 182–183, 218 (2020).

    Article  Google Scholar 

  30. N. Boechler, G. Theocharis, and C. Daraio, Bifurcation-based acoustic switching and rectification, Nat. Mater. 10, 665 (2011).

    Article  Google Scholar 

  31. L. S. Wei, Y. Z. Wang, and Y. S. Wang, Nonreciprocal transmission of nonlinear elastic wave metamaterials by incremental harmonic balance method, Int. J. Mech. Sci. 173, 105433 (2020).

    Article  Google Scholar 

  32. L. Cai, J. Yang, P. Rizzo, X. Ni, and C. Daraio, Propagation of highly nonlinear solitary waves in a curved granular chain, Granular Matter 15, 357 (2013).

    Article  Google Scholar 

  33. J. Yang, S. Dunatunga, and C. Daraio, Amplitude-dependent attenuation of compressive waves in curved granular crystals constrained by elastic guides, Acta Mech. 223, 549 (2012).

    Article  MATH  Google Scholar 

  34. Y. K. Cheung, S. H. Chen, and S. L. Lau, Application of the incremental harmonic balance method to cubic non-linearity systems, J. Sound Vib. 140, 273 (1990).

    Article  Google Scholar 

  35. S. H. Chen, Y. K. Cheung, and H. X. **ng, Nonlinear vibration of plane structures by finite element and incremental harmonic balance method, Nonlinear Dyn. 26, 87 (2001).

    Article  MATH  Google Scholar 

  36. A. A. Ferri, On the equivalence of the incremental harmonic balance method and the harmonic balance-Newton Raphson method, J. Appl. Mech. 53, 455 (2018).

    Article  MathSciNet  Google Scholar 

  37. S. Wang, L. Hua, C. Yang, X. Han, and Z. Su, Applications of incremental harmonic balance method combined with equivalent piecewise linearization on vibrations of nonlinear stiffness systems, J. Sound Vib. 441, 111 (2019).

    Article  Google Scholar 

  38. A. J. Martínez, H. Yasuda, E. Kim, P. G. Kevrekidis, M. A. Porter, and J. Yang, Scattering of waves by impurities in precompressed granular chains, Phys. Rev. E 93, 052224 (2016).

    Article  Google Scholar 

  39. E. Kim, R. Chaunsali, H. Xu, J. Jaworski, J. Yang, P. G. Kevrekidis, and A. F. Vakakis, Nonlinear low-to-high-frequency energy cascades in diatomic granular crystals, Phys. Rev. E 92, 062201 (2015).

    Article  Google Scholar 

  40. R. K. Narisetti, M. J. Leamy, and M. Ruzzene, A perturbation approach for predicting wave propagation in one-dimensional nonlinear periodic structures, J. Vib. Acoust. 132, 031001 (2010).

    Article  Google Scholar 

  41. S. Job, F. Santibanez, F. Tapia, and F. Melo, Wave localization in strongly nonlinear Hertzian chains with mass defect, Phys. Rev. E 80, 025602 (2009).

    Article  Google Scholar 

  42. Y. Man, N. Boechler, G. Theocharis, P. G. Kevrekidis, and C. Daraio, Defect modes in one-dimensional granular crystals, Phys. Rev. E 85, 037601 (2012).

    Article  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11991031 and 12021002).

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Authors and Affiliations

  1. Institute of Engineering Mechanics, Bei**g Jiaotong University, Bei**g, 100044, China

    Lin-Shuai Wei  (位琳帅) & Yue-Sheng Wang  (汪越胜)

  2. Department of Mechanics, Tian** University, Tian**, 300350, China

    Wu Zhou  (周武), Yi-Ze Wang  (**泽) & Yue-Sheng Wang  (汪越胜)

Authors
  1. Lin-Shuai Wei  (位琳帅)
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  2. Wu Zhou  (周武)
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  3. Yi-Ze Wang  (**泽)
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  4. Yue-Sheng Wang  (汪越胜)
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Contributions

Author contributions Lin-Shuai Wei performed the research and wrote the first draft of the manuscript. Wu Zhou improved the numerical calculation and expression during the revision. Yi-Ze Wang and Yue-Sheng Wang designed the research and participated in the revision of the manuscript.

Corresponding authors

Correspondence to Yi-Ze Wang  (**泽) or Yue-Sheng Wang  (汪越胜).

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Wei, LS., Zhou, W., Wang, YZ. et al. Diode behaviors of curved elastic wave metamaterials with a nonlinear granular chain. Acta Mech. Sin. 39, 723078 (2023). https://doi.org/10.1007/s10409-023-23078-x

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