A new tunable elastic metamaterial structure for manipulating band gaps/wave propagation

doi:10.1007/s10483-021-2787-8

Applied Mathematics and Mechanics (English Edition) ›› 2021, Vol. 42 ›› Issue (11): 1543-1554.doi: https://doi.org/10.1007/s10483-021-2787-8

• 论文 • 下一篇

A new tunable elastic metamaterial structure for manipulating band gaps/wave propagation

Zhenyu WANG, Zhaoyang MA, Xingming GUO, Dongsheng ZHANG

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200444, China

收稿日期:2021-08-03 修回日期:2021-09-10 出版日期:2021-11-01 发布日期:2021-10-23
通讯作者: Xingming GUO, E-mail:xmguo@shu.edu.cn
基金资助:
the National Natural Science Foundation of China (Nos. 11872233, 12102245, and 11727804)

A new tunable elastic metamaterial structure for manipulating band gaps/wave propagation

Zhenyu WANG, Zhaoyang MA, Xingming GUO, Dongsheng ZHANG

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200444, China

Received:2021-08-03 Revised:2021-09-10 Online:2021-11-01 Published:2021-10-23
Contact: Xingming GUO, E-mail:xmguo@shu.edu.cn
Supported by:
the National Natural Science Foundation of China (Nos. 11872233, 12102245, and 11727804)

摘要/Abstract

摘要： A one-dimensional mechanical lattice system with local resonators is proposed as an elastic metamaterial model, which shows negative mass and negative modulus under specific frequency ranges. The proposed representative units, consisting of accurately arranged rigid components, can generate controllable translational resonance and achieve negative mass and negative modulus by adjusting the local structural parameters. A shape memory polymer is adopted as a spring component, whose Young's modulus is obviously affected by temperature, and the proposed metamaterials' tunable ability is achieved by adjusting temperature. The effect of the shape memory polymer's stiffness variation on the band gaps is investigated detailedly, and the special phenomenon of intersecting dispersion curves is discussed, which can be designed and controlled by adjusting temperature. The dispersion relationship of the continuum metamaterial model affected by temperature is obtained, which shows great tunable ability to manipulate wave propagation.

关键词: tunable elastic metamaterial, negative mass, negative modulus

Abstract: A one-dimensional mechanical lattice system with local resonators is proposed as an elastic metamaterial model, which shows negative mass and negative modulus under specific frequency ranges. The proposed representative units, consisting of accurately arranged rigid components, can generate controllable translational resonance and achieve negative mass and negative modulus by adjusting the local structural parameters. A shape memory polymer is adopted as a spring component, whose Young's modulus is obviously affected by temperature, and the proposed metamaterials' tunable ability is achieved by adjusting temperature. The effect of the shape memory polymer's stiffness variation on the band gaps is investigated detailedly, and the special phenomenon of intersecting dispersion curves is discussed, which can be designed and controlled by adjusting temperature. The dispersion relationship of the continuum metamaterial model affected by temperature is obtained, which shows great tunable ability to manipulate wave propagation.

Key words: tunable elastic metamaterial, negative mass, negative modulus

中图分类号:

74H45

Zhenyu WANG, Zhaoyang MA, Xingming GUO, Dongsheng ZHANG. A new tunable elastic metamaterial structure for manipulating band gaps/wave propagation[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(11): 1543-1554.

参考文献

[1] WALSER, R. M. Metamaterials:what are they? what are they good for? APS March Meeting, American Physical Society, Ridge (2000)
[2] LU, L., RU, C. Q., and GUO, X. M. Negative effective mass of a filled carbon nanotube. International Journal of Mechanical Sciences, 134, 174-181(2017)
[3] WU, B., GUO, X. M., and RU, C. Q. Reduced vibrational frequencies of multiwall carbon nanotubes due to interlayer degrees of freedom. European Journal of Mechanics-A/Solids, 47, 206-210(2014)
[4] HU, Z. L., GUO, X. M., and RU, C. Q. Enhanced critical pressure for buckling of carbon nanotubes due to an inserted linear carbon chain. Nanotechnology, 19(30), 305703(2008)
[5] HU, Z. L., GUO, X. M., and RU, C. Q. The effects of an inserted linear carbon chain on the vibration of a carbon nanotube. Nanotechnology, 18(48), 485712(2007)
[6] VESELAGO, V. G. The electrodynamics of substances with simultaneously negative values of ε and μ. Soviet Physics Uspekhi, 10(4), 509-514(1968)
[7] CRASTER, R. V. and GUENNEAU, S. Acoustic Metamaterials:Negative Refraction, Imaging, Lensing and Cloaking, Springer, the Netherlands (2013)
[8] LI, Y., LIANG, B., GU, Z. M., ZOU, X. Y., and CHENG, J. C. Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces. Scientific Reports, 3, 2546(2013)
[9] LI, Y., JIANG, X., LI, R. Q., LIANG, B., ZOU, X. Y., YIN, L. L., and CHENG, J. C. Experimental realizations of full control of reflected waves with subwavelength acoustic metasurfaces. Physical Review Applied, 2(6), 064002(2014)
[10] ZHU, Y. F., ZOU, X. Y., LI, R. Q., JIANG, X., TU, J., LIANG, B., and CHENG, J. C. Dispersionless manipulation of reflected acoustic wavefront by subwavelength corrugated surface. Scientific Reports, 5, 10966(2015)
[11] ZHAO, J. J., LI, B. W., CHEN, Z. N., and QIU, C. W. Redirection of sound waves using acoustic metasurface. Applied Physics Letters, 103(15), 151604(2013)
[12] SHELBY, R. A., SMITH, D. R., and SCHULTZ, S. Experimental verification of a negative index of refraction. Science, 292, 77-79(2001)
[13] XIE, Y. B., WANG, W. Q., CHEN, H. Y., KONNEKER, A., POPA, B. I., and CUMMER, S. A. Wavefront modulation and subwavelength diffractive acoustics with an acoustic metasurface. Nature Communications, 5, 5553(2014)
[14] LIU, Z. Y., ZHANG, X. X., MAO, Y. W., ZHU, Y. Y., YANG, Z. Y., CHAN, C. T., and SHENG, P. Locally resonant sonic materials. Science, 289, 1734-1736(2000)
[15] HUSSEIN, M. I., HULBERT, G. M., and SCOTT, R. A. Dispersive elastodynamics of 1D banded materials and structures:design. Journal of Sound and Vibration, 307, 865-893(2007)
[16] KHELIF, A., CHOUJAA, A., and BENCHABANE, S. Guiding and bending of acoustic waves in highly confined photonic crystal waveguides. Applied Physics Letters, 84(22), 4400-4402(2004)
[17] LUCKLUM, R. and LI, J. Phononic crystals for liquid sensor applications. Measurement Science & Technology, 20(12), 124014(2009)
[18] LU, L., RU, C. Q., and GUO, X. M. Vibration isolation of few-layer graphene sheets. International Journal of Solids and Structures, 185-186, 78-88(2020)
[19] MILTON, G. W. and WILLIS, J. R. On modifications of Newton's second law and linear continuum elastodynamics. Proceedings of the Royal Society A, 463, 855-880(2007)
[20] CUMMER, S. A., CHRISTENSEN, J., and ALÙ, A. Controlling sound with acoustic metamaterials. Nature Reviews Materials, 1(3), 16001(2016)
[21] AN, X. Y., LAI, C. L., FAN, H. L., and ZHANG, C. Z. 3D acoustic metamaterial-based mechanical metalattice structures for low-frequency and broadband vibration attenuation. International Journal of Solids and Structures, 191, 293-306(2020)
[22] ZHANG, Y. Y., GAO, N. S., and WU, J. H. New mechanism of tunable broadband in local resonance structures. Applied Acoustics, 169, 107482(2020)
[23] HU, X. H., HO, K. M., CHAN, C. T., and ZI, J. Homogenization of acoustic metamaterials of Helmholtz resonators in fluid. Physical Review, 77, 21-24(2008)
[24] STARKEY, T. A., SMITH, J. D., HIBBINS, A. P., SAMBLES, J. R., and RANEE, H. J. Thin structured rigid body for acoustic absorption. Applied Physics Letters, 110, 041902(2017)
[25] CLIMENTE, A., TORRENT, D., and SÁNCHEZ-DEHESA, J. Omnidirectional broadband acoustic absorber based on metamaterials. Applied Physics Letters, 100, 144103(2012)
[26] ZHU, R., CHEN, Y. Y., BARNHART, M. V., HU, G. K., SUN, C. T., and HUANG, G. L. Experimental study of an adaptive elastic metamaterial controlled by electric circuits. Applied Physics Letters, 108, 1734-1736(2016)
[27] SHIGA, T., OKADA, A., and KURAUCHI, T. Magnetroviscoelastic behavior of composite gels. Journal of Applied Polymer Science, 58(4), 787-792(1995)
[28] YOON, J. Y., HONG, S. W., PARK, Y. J., KIM, S. H., KIM, G. W., and CHOI, S. B. Tunable Young's moduli of soft composites fabricated from magnetorheological materials containing microsized iron particles. Materials, 13, 3378(2020)
[29] CHEN, H. J., ZHAO, W. X., and HAO, C. C. Tunable broadband sound absorbing metamaterial with negative modulus. Chinese Journal of Liquid Crystals and Displays, 30, 234-239(2015)
[30] ZHANG, S., ZHOU, J. F., PARK, Y. S., RHO, J., SINGH, R., NAM, S., AZAD, A. K., CHEN, H. T., YIN, X. B., TAYLOR, A. J., and ZHANG, X. Photoinduced handedness switching in terahertz chiral metamolecules. Nature Communications, 3, 942-949(2012)
[31] CHEN, Z., XUE, C., FAN, L., ZHANG, S. Y., LI, X. J., ZHANG, H., and DING, J. A tunable acoustic metamaterial with double-negativity driven by electromagnets. Scientific Reports, 6, 30254(2016)
[32] MA, G., FAN, X., SHENG, P., and FINK, M. Shaping reverberating sound fields with an actively tunable metasurface. Proceedings of the National Academy of Sciences, 115, 6638-6643(2018)
[33] WANG, X. J., GUO, X. G., YE, J. L., ZHENG, N., KOHLI, P., CHOI, D., ZHANG, Y., XIE, Z. Q., ZHANG, Q. H., LUAN, H. W., NAN, K. W., KIM, B. H., XU, Y. M., SHAN, X. W., BAI, W. B., SUN, R. J., WANG, Z. Z., JANG, H., ZHANG, F., MA, Y. J., XU, Z., FENG, X., XIE, T., HUANG, Y. G., ZHANG, Y. H., and ROGERS, J. A. Freestanding 3D mesostructures, functional devices, and shape-programmable systems based on mechanically induced assembly with shape memory polymers. Advanced Materials, 31, 1805615(2019)
[34] LIU, Y. Q., SU, X. Y., and SUN, C. T. Broadband elastic metamaterial with single negativity by mimicking lattice systems. Journal of the Mechanics and Physics of Solids, 74, 158-174(2015)
[35] YI, J. L., NEGAHBAN, M., LI, Z., SU, X. Y., and XIA, R. Y. Conditionally extraordinary transmission in periodic parity-time symmetric phononic crystals. International Journal of Mechanical Sciences, 163, 105134(2019)

A new tunable elastic metamaterial structure for manipulating band gaps/wave propagation

A new tunable elastic metamaterial structure for manipulating band gaps/wave propagation

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