Modeling and analysis of gradient metamaterials for broad fusion bandgaps

doi:10.1007/s10483-024-3154-6

摘要/Abstract

Abstract:

A gradient metamaterial with varying-stiffness local resonators is proposed to open the multiple bandgaps and further form a broad fusion bandgap. First, three local resonators with linearly increasing stiffness are periodically attached to the spring-mass chain to construct the gradient metamaterial. The dispersion relation is then derived based on Bloch's theorem to reveal the fusion bandgap theoretically. The dynamic characteristic of the finite spring-mass chain is investigated to validate the fusion of multiple bandgaps. Finally, the effects of the design parameters on multiple bandgaps are discussed. The results show that the metamaterial with a non-uniform stiffness gradient pattern is capable of opening a broad fusion bandgap and effectively attenuating the longitudinal waves within a broad frequency region.

Key words: local resonance mechanism, elastic metamaterial, stiffness gradient, bandgap fusion, broadband wave attenuation

中图分类号:

74H45
74J05

. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(7): 1155-1170.

Changqi CAI, Chenjie ZHU, Fengyi ZHANG, Jiaojiao SUN, Kai WANG, Bo YAN, Jiaxi ZHOU. Modeling and analysis of gradient metamaterials for broad fusion bandgaps[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(7): 1155-1170.

图/表 12

参考文献 42

1	WANG, K., ZHOU, J. X., TAN, D. G., LI, Z. Y., LIN, Q. D., and XU, D. L. A brief review of metamaterials for opening low-frequency band gaps. Applied Mathematics and Mechanics (English Edition), 43 (7), 1125- 1144 (2022) doi: 10.1007/s10483-022-2870-9
2	HU, G. B., TANG, L. H., LIANG, J. R., LAN, C. B., and DAS, R. Acoustic-elastic metamaterials and phononic crystals for energy harvesting: a review. Smart Materials and Structures, 30, 085025 (2021)
3	CHEN, K. K., DONG, X. J., GAO, P. L., ZHANG, J. Y., SUN, Y. T., TU, G. W., and PENG, Z. K. Multifunctional applications of topological valley-locked elastic waves. International Journal of Mechanical Sciences, 259, 108589 (2023)
4	CHEN, Y. Y., and WANG, L. F. Multiband wave filtering and waveguiding in bio-inspired hierarchical composites. Extreme Mechanics Letters, 5, 18- 24 (2015)
5	DONG, X. J., CHEN, K. K., ZHANG, J., HUANGFU, Y. F., and PENG, Z. K. Topological valley mode separation of elastic waves and potential applications. International Journal of Mechanical Sciences, 274, 109229 (2024)
6	XI, C. Y., DOU, L. L., MI, Y. Z., and ZHENG, H. Inertial amplification induced band gaps in corrugated-core sandwich panels. Composite Structures, 267, 113918 (2021)
7	MARTÍNEZ-SALA, R., SANCHO, J., SÁNCHEZ, J. V., GÓMEZ, V., LLINARES, J., and MESEGUER, F. Sound attenuation by sculpture. nature, 378 (6554), 241 (1995)
8	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 (5485), 1734- 1736 (2000)
9	XIAO, Y., WEN, J. H., WANG, G., and WEN, X. S. Theoretical and experimental study of locally resonant and bragg band gaps in flexural beams carrying periodic arrays of beam-like resonators. Journal of Vibration and Acoustics, Transactions of the ASME, 135 (4), 041006 (2013)
10	YU, D. L., LIU, Y. Z., WANG, G., ZHAO, H. G., and QIU, J. Flexural vibration band gaps in Timoshenko beams with locally resonant structures. Journal of Applied Physics, 100 (12), 124901 (2006)
11	YU, D. L., WEN, J. H., ZHAO, H. G., LIU, Y. Z., and WEN, X. S. Vibration reduction by using the idea of phononic crystals in a pipe-conveying fluid. Journal of Sound and Vibration, 318 (1-2), 193- 205 (2008)
12	SONG, Y. B., FENG, L. P., LIU, Z. B., WEN, J. H., and YU, D. L. Suppression of the vibration and sound radiation of a sandwich plate via periodic design. International Journal of Mechanical Sciences, 150, 744- 754 (2019)
13	WANG, K., ZHOU, J. X., XU, D. L., and OUYANG, H. J. 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)
14	YU, D. L., LIU, Y. Z., WANG, G., CAI, L., and QIU, J. Low frequency torsional vibration gaps in the shaft with locally resonant structures. Physics Letters A, 348, 410- 415 (2006)
15	ZHAO, L., LU, Z. Q., DING, H., and CHEN, L. Q. Experimental observation of transverse and longitudinal wave propagation in a metamaterial periodically arrayed with nonlinear resonators. Mechanical Systems and Signal Processing, 170, 108836 (2022)
16	LU, Z. Q., ZHAO, L., DING, H., and CHEN, L. Q. A dual-functional metamaterial for integrated vibration isolation and energy harvesting. Journal of Sound and Vibration, 509, 116251 (2021)
17	FERNANDES, R., EL-BORGI, S., YAZBECK, R., BOYD, J. G., and LAGOUDAS, D. C. Non-dimensional analysis of the bandgap formation in a locally resonant metamaterial pipe conveying fluid. Applied Mathematical Modelling, 106, 241- 258 (2022)
18	YU, D. L., WEN, J. H., ZHAO, H. G., LIU, Y. Z., and WEN, X. S. Flexural vibration band gap in a periodic fluid-conveying pipe system based on the Timoshenko beam theory. Journal of Vibration and Acoustics, 133, 014502 (2011)
19	LI, Z. Y., MA, T. X., WANG, Y. Z., CHAI, Y. Y., ZHANG, C. Z., and LI, F. M. Active auto-adaptive metamaterial plates for flexural wave control. International Journal of Solids and Structures, 254, 111865 (2022)
20	LI, J. Q., XUE, Y., and LI, F. M. Active band gap control of magnetorheological meta-plate using frequency feedback control law. Journal of Sound and Vibration, 567, 118076 (2023)
21	YAO, D. H., XIONG, M. K., LUO, J. Y., and YAO, L. Y. Flexural wave mitigation in metamaterial cylindrical curved shells with periodic graded arrays of multi-resonator. Mechanical Systems and Signal Processing, 168, 108721 (2022)
22	LU, K., ZHOU, G. J., GAO, N. S., LI, L. Z., LEI, H. X., and YU, M. R. Flexural vibration bandgaps of the multiple local resonance elastic metamaterial plates with irregular resonators. Applied Acoustics, 159, 107115 (2020)
23	ZHANG, H., XIAO, Y., WEN, J. H., YU, D. L., and WEN, X. S. Flexural wave band gaps in metamaterial beams with membrane-type resonators: theory and experiment. Journal of Physics D: Applied Physics, 48 (43), 435305 (2015)
24	LI, J. Q., FAN, X. L., and LI, F. M. Numerical and experimental study of a sandwich-like metamaterial plate for vibration suppression. Composite Structures, 238, 111969 (2020)
25	LI, H., HU, Y. B., HUANG, H. Y., CHEN, J. L., ZHAO, M. Y., and LI, B. Broadband low-frequency vibration attenuation in 3D printed composite meta-lattice sandwich structures. Composites Part B: Engineering, 215, 108772 (2021)
26	WU, Z. J., LIU, W. Y., LI, F. M., and ZHANG, C. Z. Band-gap property of a novel elastic metamaterial beam with X-shaped local resonators. Mechanical Systems and Signal Processing, 134, 106357 (2019)
27	JIANG, T. X., and HE, Q. B. Dual-directionally tunable metamaterial for low-frequency vibration isolation. Applied Physics Letters, 110 (2), 021907 (2017)
28	JIN, G. X., WANG, Z. H., and YANG, T. Z. Cascaded quasi-zero stiffness nonlinear low-frequency vibration isolator inspired by human spine. Applied Mathematics and Mechanics (English Edition), 43 (6), 813- 824 (2022) doi: 10.1007/s10483-022-2852-5
29	LU, Z. Q., BRENNAN, M., DING, H., and CHEN, L. Q. High-static-low-dynamic-stiffness vibration isolation enhanced by damping nonlinearity. Science China Technological Sciences, 62 (7), 1103- 1110 (2019)
30	ZHOU, J. X., WANG, K., XU, D. L., and OUYANG, H. J. Local resonator with high-static-low-dynamic stiffness for lowering band gaps of flexural wave in beams. Journal of Applied Physics, 121 (4), 044902 (2017)
31	FANG, X., WEN, J. H., BONELLO, B., YIN, J. F., and YU, D. L. Ultra-low and ultra-broad-band nonlinear acoustic metamaterials. Nature Communications, 8 (1), 1288 (2017)
32	CHENG, Q., GUO, H., YUAN, T., SUN, P., GUO, F. X., and WANG, Y. S. Topological design of square lattice structure for broad and multiple band gaps in low-frequency range. Extreme Mechanics Letters, 35, 100632 (2020)
33	XIAO, Y., WEN, J. H., YU, D. L., and WEN, X. S. Flexural wave propagation in beams with periodically attached vibration absorbers: band-gap behavior and band formation mechanisms. Journal of Sound and Vibration, 332 (4), 867- 893 (2013)
34	GAO, Y. Q., and WANG, L. F. Nonlocal active metamaterial with feedback control for tunable bandgap and broadband nonreciprocity. International Journal of Mechanical Sciences, 219, 107131 (2022)
35	LI, C., JIANG, T. X., HE, Q. B., and PENG, Z. K. Stiffness-mass-coding metamaterial with broadband tunability for low-frequency vibration isolation. Journal of Sound and Vibration, 489, 115685 (2020)
36	TIAN, Y. J., WU, J. H., LI, H. L., GU, C. S., YANG, Z. R., ZHAO, Z. T., and LU, K. Elastic wave propagation in the elastic metamaterials containing parallel multi-resonators. Journal of Physics D: Applied Physics, 52 (39), 395301 (2019)
37	GAO, Y. Q., and WANG, L. F. Ultrawide coupled bandgap in hybrid periodic system with multiple resonators. Journal of Applied Physics, 127 (20), 204901 (2020)
38	WANG, L. Z., CHEN, Z. B., and CHENG, L. A metamaterial plate with magnetorheological elastomers and gradient resonators for tuneable, low-frequency and broadband flexural wave manipulation. Thin-Walled Structures, 184, 110521 (2023)
39	CHEN, T. G., XIA, B. Z., YU, D. J., and BI, C. X. Robust enhanced acoustic sensing via gradient phononic crystals. Physics Letters A, 493, 129242 (2024)
40	HU, G. B., AUSTIN, A. C. M., SOROKIN, V., and TANG, L. H. Metamaterial beam with graded local resonators for broadband vibration suppression. Mechanical Systems and Signal Processing, 146, 106982 (2021)
41	WU, X. Y., WEN, Z. H., JIN, Y. B., RABCZUK, T. M., ZHUANG, X. Y., and DJAFARI-ROUHANI, B. Broadband Rayleigh wave attenuation by gradient metamaterials. International Journal of Mechanical Sciences, 205, 106592 (2021)
42	DOYLE, J. F. Wave Propagation in Structures, Springer, New York (1989)

[1]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(12): 2075-2092.
[2]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(11): 1987-2010.
[3]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(11): 1949-1964.
[4]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(11): 1895-1912.
[5]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(10): 1807-1820.
[6]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(10): 1749-1772.
[7]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(9): 1595-1612.
[8]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(9): 1539-1556.
[9]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(8): 1403-1414.
[10]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(8): 1295-1314.
[11]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(7): 1107-1118.
[12]	Shuo WANG, Anshuai WANG, Yansen WU, Xiaofeng LI, Yongtao SUN, Zhaozhan ZHANG, Qian DING, G. D. AYALEW, Yunxiang MA, Qingyu LIN. Ultra-wide band gap and wave attenuation mechanism of a novel star-shaped chiral metamaterial[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(7): 1261-1278.
[13]	Yiming CAO, Hui MA, Xumin GUO, Bingfeng ZHAO, Hui LI, Xin WANG, Bing WANG. Comparison of nonlinear modeling methods for the composite rubber clamp[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(5): 763-778.
[14]	Lele REN, Wei ZHANG, Ting DONG, Yufei ZHANG. Snap-through behaviors and nonlinear vibrations of a bistable composite laminated cantilever shell:an experimental and numerical study[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(5): 779-794.
[15]	Jinghu TANG, Chaofeng LI, Jin ZHOU, Zhiwei WU. Research on modeling and self-excited vibration mechanism in magnetic levitation-collision interface coupling system[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(5): 873-890.