A brief review of metamaterials for opening low-frequency band gaps

doi:10.1007/s10483-022-2870-9

Abstract

Abstract: Metamaterials are an emerging type of man-made material capable of obtaining some extraordinary properties that cannot be realized by naturally occurring materials. Due to tremendous application foregrounds in wave manipulations, metamaterials have gained more and more attraction. Especially, developing research interest of low-frequency vibration attenuation using metamaterials has emerged in the past decades. To better understand the fundamental principle of opening low-frequency (below 100 Hz) band gaps, a general view on the existing literature related to low-frequency band gaps is presented. In this review, some methods for fulfilling low-frequency band gaps are firstly categorized and detailed, and then several strategies for tuning the low-frequency band gaps are summarized. Finally, the potential applications of this type of metamaterial are briefly listed. This review is expected to provide some inspirations for realizing and tuning the low-frequency band gaps by means of summarizing the related literature.

Key words: metamaterial, low-frequency, band gap, vibration suppression

2010 MSC Number:

70K30
74H45

Kai WANG, Jiaxi ZHOU, Dongguo TAN, Zeyi LI, Qida LIN, Daolin XU. A brief review of metamaterials for opening low-frequency band gaps. Applied Mathematics and Mechanics (English Edition), 2022, 43(7): 1125-1144.

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URL: https://www.amm.shu.edu.cn/EN/10.1007/s10483-022-2870-9

https://www.amm.shu.edu.cn/EN/Y2022/V43/I7/1125

References

[1] ZIANNI, X. Thermoelectric metamaterials:nano-waveguides for thermoelectric energy conversion and heat management at the nanoscale. Advanced Electronic Materials, 7, 1-16(2021)
[2] ENGHETA, N. and ZIOLKOWSKI, R. W. Metamaterials:Physics and Engineering Explorations, Wiley-IEEE Press, New York (2017)[1] ZIANNI, X. Thermoelectric metamaterials:nano-waveguides for thermoelectric energy conversion and heat management at the nanoscale. Advanced Electronic Materials, 7, 1-16(2021)
[2] ENGHETA, N. and ZIOLKOWSKI, R. W. Metamaterials:Physics and Engineering Explorations, Wiley-IEEE Press, New York (2017) A brief review of metamaterials for opening low-frequency band gaps 1139
[3] ZOUHDI, S., SIHVOLA, A., and VINOGRADOV, A. P. Metamaterials and Plasmonics:Fundamentals, Modelling, Applications, Springer Science&Business Media, Dordrecht (2008)
[4] WANG, Y., ZHAO, W., RIMOLI, J. J., ZHU, R., and HU, G. Prestress-controlled asymmetric wave propagation and reciprocity-breaking in tensegrity metastructure. Extreme Mechanics Letters, 37, 100724(2020)
[5] JI, J. C., LUO, Q., and YE, K. Vibration control based metamaterials and origami structures:a state-of-the-art review. Mechanical Systems and Signal Processing, 161, 107945(2021)
[6] TANG, L. and CHENG, L. Impaired sound radiation in plates with periodic tunneled acoustic black holes. Mechanical Systems and Signal Processing, 135, 106410(2020)
[7] FLEURY, R., MONTICONE, F., and ALU A. Invisibility and cloaking:origins, present, and`future perspectives. Physical Review Applied, 4, 037001(2015)
[8] FANG, X., WEN, J., BENISTY, H., and YU, D. Ultrabroad acoustical limiting in nonlinear metamaterials due to adaptive-broadening band-gap effect. Physical Review B, 101, 104304(2020)
[9] CHEN, Y., HU, G., and HUANG, G. A hybrid elastic metamaterial with negative mass density and tunable bending stiffness. Journal of the Mechanics and Physics of Solids, 105, 179-198(2017)
[10] KACIN, S., OZTURK, M., SEVIM, U. K., MERT, B. A., OZER, Z., AKGOL, O., UNAL, E., and KARAASLAN, M. Seismic metamaterials for low-frequency mechanical wave attenuation. Natural Hazards, 107, 213-229(2021)
[11] MA, G. and SHENG, P. Acoustic metamaterials:from local resonances to broad horizons. Science Advances, 2, 1501595(2016)
[12] JOHN, S. Strong localization of photons in certain disordered dielectric superlattices. Physical Review Letters, 58, 2486-2489(1987)
[13] LEMOULT, F., KAINA, N., FINK, M., and LEROSEY, G. Wave propagation control at the deep subwavelength scale in metamaterials. Nature Physics, 9, 55-60(2012)
[14] MART′ INEZ-SALA, R., SANCHO, J., SANCHEZ, J. V., GOMEZ, V., LLINARES, J., andMESEGUER, F. Sound attenuation by sculpture. nature, 378, 241-241(1995)
[15] WU, L., WANG, Y., CHUANG, K., WU, F., WANG, Q., LIN, W., and JIANG, H. A brief review of dynamic mechanical metamaterials for mechanical energy manipulation. Materials Today, 44, 168-193(2021)
[16] LIU, Z., ZHANG, X., MAO, Y., ZHU, Y. Y., YANG, Z., CHAN, C. T., and SHENG, P. Locally resonant sonic materials. Science, 289, 1734-1736(2000)
[17] YAN, B., WANG, Z., MA, H., BAO, H., WANG, K., and WU, C. A novel lever-type vibration isolator with eddy current damping. Journal of Sound and Vibration, 494, 115862(2021)
[18] WANG, K., ZHOU, J., OUYANG, H., CHANG, Y., and XU, D. A dual quasi-zero-stiffness sliding-mode triboelectric nanogenerator for harvesting ultralow-low frequency vibration energy. Mechanical Systems and Signal Processing, 151, 107368(2021)
[19] WANG, K., ZHOU, J., and XU, D. Sensitivity analysis of parametric errors on the performance of a torsion quasi-zero-stiffness vibration isolator. International Journal of Mechanical Sciences, 134, 336-346(2017)
[20] YAN, B., MA, H., ZHANG, L., ZHENG, W., WANG, K., and WU, C. A bistable vibration isolator with nonlinear electromagnetic shunt damping. Mechanical Systems and Signal Processing, 136, 106504(2020)
[21] WANG, K., OUYANG, H., ZHOU, J., CHANG, Y., XU, D., and ZHAO, H. A nonlinear hybrid energy harvester with high ultralow-frequency energy harvesting performance. Meccanica, 56, 461-480(2021)
[22] WANG, K., ZHOU, J. X., XU, D. L., and OUYANG, H. J. Tunable low-frequency torsional-wave band gaps in a meta-shaft. Journal of Physics D:Applied Physics, 52, 055104(2019)
[23] GUO, L., WANG, X., FAN, R. L., and BI, F. Review on development of high-static-low-dynamicstiffness seat cushion mattress for vibration control of seating suspension system. Applied Sciences, 10, 2887(2020)
[24] BANG, S., KIM, J., YOON, G., TANAKA, T., and RHO, J. Recent advances in tunable and reconfigurable metamaterials. Micromachines, 9, 560(2018)
[25] YU, D., LIU, Y., WANG, G., ZHAO, H., and QIU, J. Flexural vibration band gaps in Timoshenko beams with locally resonant structures. Journal of Applied Physics, 100, 124901(2006)
[26] FANG, X., WEN, J., BONELLO, B., YIN, J., and YU, D. Ultra-low and ultra-broad-band nonlinear acoustic metamaterials. Nature Communications, 8, 1-11(2017)
[27] BILAL, O. R., FOEHR, A., and DARAIO, C. Enhancement of deep-subwavelength band gaps in flat spiral-based phononic metamaterials using the trampoline phenomena. Journal of Applied Mechanics, 87, 071009(2020)
[28] ATTARZADEH, M. A., CALLANAN, J., and NOUH, M. Experimental observation of nonreciprocal waves in a resonant metamaterial beam. Physical Review Applied, 13, 021001(2020)
[29] SALARI-SHARIF, L., HAGHPANAH, B., GUELL IZARD, A., TOOTKABONI, M., and VALDEVIT, L. Negative-stiffness inclusions as a platform for real-time tunable phononic metamaterials. Physical Review Applied, 11, 024062(2019)
[30] TAN, X., CHEN, S., WANG, B., TANG, J., WANG, L., ZHU, S., YAO, K., and XU, P. Realtime tunable negative stiffness mechanical metamaterial. Extreme Mechanics Letters, 41, 100990(2020)
[31] FRAZIER, M. J. and KOCHMANN, D. M. Band gap transmission in periodic bistable mechanical systems. Journal of Sound and Vibration, 388, 315-326(2016)
[32] LI, S., DOU, Y., CHEN, T., XU, J., LI, B., and ZHANG, F. Designing a broad locally-resonant bandgap in a phononic crystals. Physics Letters A, 383, 1371-1377(2019)
[33] XU, X., BARNHART, M. V., FANG, X., WEN, J., CHEN, Y., and HUANG, G. A nonlinear dissipative elastic metamaterial for broadband wave mitigation. International Journal of Mechanical Sciences, 164, 105159(2019)
[34] PATTERSON, J. D. and BAILEY, B. C. Solid-State Physics:Introduction to the Theory, Springer, New York (2007)
[35] JENSEN, J. S. Phononic band gaps and vibrations in one-and two-dimensional mass-spring structures. Journal of Sound and Vibration, 266, 1053-1078(2003)
[36] LAZAROV, B. S. and JENSEN, J. S. Low-frequency band gaps in chains with attached nonlinear oscillators. International Journal of Non-Linear Mechanics, 42, 1186-1193(2007)
[37] XIAO, Y., WEN, J., and WEN, X. Flexural wave band gaps in locally resonant thin plates with periodically attached springmass resonators. Journal of Physics D:Applied Physics, 45, 195401(2012)
[38] HUSSEIN, M. I., LEAMY, M. J., and RUZZENE, M. Dynamics of phononic materials and structures:historical origins, recent progress, and future outlook. Applied Mechanics Reviews, 66, 040802(2014)
[39] OH, J. H., CHOI, S. J., LEE, J. K., and KIM, Y. Y. Zero-frequency Bragg gap by spin-harnessed metamaterial. New Journal of Physics, 20, 083035(2018)
[40] OH, J. H. and ASSOUAR, B. Quasi-static stop band with flexural metamaterial having zero rotational stiffness. Scientific Reports, 6, 33410(2016)
[41] PARK, S. and JEON, W. Ultra-wide low-frequency band gap in a tapered phononic beam. Journal of Sound and Vibration, 499, 115977(2021)
[42] ZHANG, Y. Y., WU, J. H., HU, G. Z., and WANG, Y. C. Flexural wave suppression by an elastic metamaterial beam with zero bending stiffness. Journal of Applied Physics, 121, 134902(2017)
[43] KADIC, M., BUCKMANN, T., STENGER, N., THIEL, M., and WEGENER, M. On the practicability of pentamode mechanical metamaterials. Applied Physics Letters, 100, 191901(2012)
[44] HUANG, Y. and ZHANG, X. Pentamode metamaterials with ultra-low-frequency single-mode band gap based on constituent materials. Journal of Physics:Condensed Matter, 33, 185703(2021)
[45] WANG, Z., CHU, Y., CAI, C., LIU, G., and WANG, M. R. Composite pentamode metamaterials with low frequency locally resonant characteristics. Journal of Applied Physics, 122, 025114(2017)46] CAI, C., HAN, C., WU, J., WANG, Z., and ZHANG, Q. Tuning method of phononic band gaps of locally resonant pentamode metamaterials. Journal of Physics D:Applied Physics, 52, 045601(2019)
[47] CAI, C., WANG, Z., CHU, Y., LIU, G., and XU, Z. The phononic band gaps of Bragg scattering and locally resonant pentamode metamaterials. Journal of Physics D:Applied Physics, 50, 415105(2017)
[48] ZHENG, B. and XU, J. Mechanical logic switches based on DNA-inspired acoustic metamaterials with ultrabroad low-frequency band gaps. Journal of Physics D:Applied Physics, 50, 465601(2017)
[49] NING, S., YANG, F., LUO, C., LIU, Z., and ZHUANG, Z. Low-frequency tunable locally resonant band gaps in acoustic metamaterials through large deformation. Extreme Mechanics Letters, 35, 100623(2020)
[50] ZHANG, H., XIAO, Y., WEN, J., YU, D., and WEN, X. Flexural wave band gaps in metamaterial beams with membrane-type resonators:theory and experiment. Journal of Physics D:Applied Physics, 48, 435305(2015)
[51] LU, K., ZHOU, G., GAO, N., LI, L., LEI, H., and YU, M. Flexural vibration bandgaps of the multiple local resonance elastic metamaterial plates with irregular resonators. Applied Acoustics, 159, 107115(2020)
[52] LI, J., FAN, X., and LI, F. Numerical and experimental study of a sandwich-like metamaterial plate for vibration suppression. Composite Structures, 238, 111969(2020)
[53] JIANG, T. and HE, Q. Dual-directionally tunable metamaterial for low-frequency vibration isolation. Applied Physics Letters, 110, 2-6(2017)
[54] TIAN, Y., WU, J. H., LI, H., GU, C., YANG, Z., ZHAO, Z., and LU, K. Elastic wave propagation in the elastic metamaterials containing parallel multi-resonators. Journal of Physics D:Applied Physics, 52, 395301(2019)
[55] MUHAMMAD and LIM, C. W. Elastic waves propagation in thin plate metamaterials and evidence of low frequency pseudo and local resonance bandgaps. Physics Letters A, 383, 2789-2796(2019)
[56] ZHANG, Y. Y., GAO, N. S., and WU, J. H. New mechanism of tunable broadband in local resonance structures. Applied Acoustics, 169, 107482(2020)
[57] FAN, L., HE, Y., CHEN, X., and ZHAO, X. Elastic metamaterial shaft with a stack-like resonator for low-frequency vibration isolation. Journal of Physics D:Applied Physics, 53, 105101(2020)
[58] MA, F., WANG, C., LIU, C., and WU, J. H. Structural designs, principles, and applications of thin-walled membrane and plate-type acoustic/elastic metamaterials. Journal of Applied Physics, 129, 231103(2021)
[59] MIAO, L., LI, C., LEI, L., FANG, H., and LIANG, X. A new periodic structure composite material with quasi-phononic crystals. Physics Letters A, 384, 126594(2020)
[60] WANG, K., ZHOU, J., CHANG, Y., OUYANG, H., XU, D., and YANG, Y. A nonlinear ultralow-frequency vibration isolator with dual quasi-zero-stiffness mechanism. Nonlinear Dynamics, 101, 755-773(2020)
[61] HU, F. and JING, X. A 6-DOF passive vibration isolator based on Stewart structure with Xshaped legs. Nonlinear Dynamics, 91, 157-185(2018)
[62] SUN, X., XU, J., and FU, J. The effect and design of time delay in feedback control for a nonlinear isolation system. Mechanical Systems and Signal Processing, 87, 206-217(2017)
[63] DING, H. and CHEN, L. Q. Nonlinear vibration of a slightly curved beam with quasi-zerostiffness isolators. Nonlinear Dynamics, 95, 2367-2382(2019)
[64] ZHAO, F., JI, J. C., YE, K., and LUO, Q. Increase of quasi-zero stiffness region using two pairs of oblique springs. Mechanical Systems and Signal Processing, 144, 106975(2020)
[65] ZHOU, J., WANG, K., XU, D., and OUYANG, H. Local resonator with high-static-low-dynamic stiffness for lowering band gaps of flexural wave in beams. Journal of Applied Physics, 121, 044902(2017)
[66] WANG, K., ZHOU, J., XU, D., and OUYANG, H. Lower band gaps of longitudinal wave in a one-dimensional periodic rod by exploiting geometrical nonlinearity. Mechanical Systems and Signal Processing, 124, 664-678(2019)
[67] WU, Z., LIU, W., LI, F., and ZHANG, C. Band-gap property of a novel elastic metamaterial beam with X-shaped local resonators. Mechanical Systems and Signal Processing, 134, 106357(2019)
[68] WANG, K., ZHOU, J., WANG, Q., OUYANG, H., and XU, D. Low-frequency band gaps in a metamaterial rod by negative-stiffness mechanisms:design and experimental validation. Applied Physics Letters, 114, 251902(2019)
[69] WANG, K., ZHOU, J., CAI, C., XU, D., XIA, S., and WEN, G. Bidirectional deep-subwavelength band gap induced by negative stiffness. Journal of Sound and Vibration, 515, 116474(2021)
[70] CAI, C., ZHOU, J., WU, L., WANG, K., XU, D., and OUYANG, H. Design and numerical validation of quasi-zero-stiffness metamaterials for very low-frequency band gaps. Composite Structures, 236, 111862(2020)
[71] ZHOU, J., PAN, H., CAI, C., and XU, D. Tunable ultralow frequency wave attenuations in onedimensional quasi-zero-stiffness metamaterial. International Journal of Mechanics and Materials in Design, 17, 285-300(2021)
[72] LIN, Q., ZHOU, J., PAN, H., XU, D., and WEN, G. Numerical and experimental investigations on tunable low-frequency locally resonant metamaterials. Acta Mechanica Solida Sinica, 34, 612-623(2021)
[73] WANG, K., ZHOU, J., OUYANG, H., CHENG, L., and XU, D. A semi-active metamaterial beam with electromagnetic quasi-zero-stiffness resonators for ultralow-frequency band gap tuning. International Journal of Mechanical Sciences, 176, 105548(2020)
[74] ZHANG, Q., GUO, D., and HU, G. Tailored mechanical metamaterials with programmable quasi-zero-stiffness features for full-band vibration isolation. Advanced Functional Materials, 31, 2101428(2021)
[75] WANG, Z., ZHANG, Q., ZHANG, K., and HU, G. Tunable digital metamaterial for broadband vibration isolation at low frequency. Advanced Materials, 28, 9857-9861(2016)
[76] ZHANG, Q., ZHANG, K., and HU, G. Tunable fluid-solid metamaterials for manipulation of elastic wave propagation in broad frequency range. Applied Physics Letters, 112, 221906(2018)
[77] ZHOU, J. X., DOU, L. L., WANG, K., XU, D. L., and OUYANG, H. J. A nonlinear resonator with inertial amplification for very low-frequency flexural wave attenuations in beams. Nonlinear Dynamics, 96, 647-665(2019)
[78] WANG, S., WANG, M., and GUO, Z. Adjustable low-frequency bandgap of flexural wave in an Euler-Bernoulli meta-beam with inertial amplified resonators. Physics Letters A, 417, 127671(2021)
[79] YILMAZ, C., HULBERT, G. M., and KIKUCHI, N. Phononic band gaps induced by inertial amplification in periodic media. Physical Review B, 76, 054309(2007)
[80] TANIKER, S. and YILMAZ, C. Generating ultra wide vibration stop bands by a novel inertial amplification mechanism topology with flexure hinges. International Journal of Solids and Structures, 106-107, 129-138(2017)
[81] FRANDSEN, N. M. M., BILAL, O. R., JENSEN, J. S., and HUSSEIN, M. I. Inertial amplification of continuous structures:large band gaps from small masses. Journal of Applied Physics, 119, 124902(2016)
[82] WU, L., WANG, Y., ZHAI, Z., YANG, Y., KRISHNARAJU, D., LU, J., WU, F., WANG, Q., and JIANG, H. Mechanical metamaterials for full-band mechanical wave shielding. Applied Materials Today, 20, 100671(2020)
[83] HU, G., AUSTIN, A. C. M., SOROKIN, V., and TANG, L. Metamaterial beam with graded local resonators for broadband vibration suppression. Mechanical Systems and Signal Processing, 146, 106982(2021)
[84] YAN, Z. and WU, J. Ultra-low-frequency broadband of a new-type acoustic metamaterial beams with stiffness array. Journal of Physics D:Applied Physics, 50, 355104(2017)
[85] ANVAR, V. Vibration isolating metamaterial with arc-structure. IOP Conference Series:Materials Science and Engineering, 225, 012142(2017)
[86] YOO, J. and PARK, N. C. Bandgap analysis of a tunable elastic-metamaterial-based vibration absorber with electromagnetic stiffness. Microsystem Technologies, 26, 3339-3348(2020)