Applied Mathematics and Mechanics (English Edition) ›› 2022, Vol. 43 ›› Issue (7): 1125-1144.doi: https://doi.org/10.1007/s10483-022-2870-9
• Articles • Previous Articles
Kai WANG1,2, Jiaxi ZHOU1, Dongguo TAN1, Zeyi LI1, Qida LIN1, Daolin XU1
Received:
2021-10-29
Revised:
2022-01-03
Online:
2022-07-01
Published:
2022-06-30
Contact:
Jiaxi ZHOU, E-mail: jxizhou@hnu.edu.cn
Supported by:
2010 MSC Number:
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.
[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) |
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