Effect of Boundary Load on Bandgaps of Elliptical Perforated-Hierarchical Panel Metamaterials

Abstract

Abstract: A hierarchical elliptical perforated-panel metamaterial (HEPMM) is proposed to investigate the effect of boundary load on its bandgaps (BGs). In this research, the boundary load was applied directly to the boundary of HEPMM, and the finite element method was adopted to study the effect of BGs with structural deformation which caused by the boundary load. Three-dimensional finite element models of different hierarchical elliptical perforated panels were established, and simplified into two-dimensional structure to investigate the in-plane bandgap characteristics conveniently. Then, the bandgap characteristics, transmission loss and different vibration modes of HEPMM with and without boundary load were simulated and analyzed. According to the results, the BGs frequencies are reduced by introducing hierarchy. Meanwhile, full BGs and directional BGs are additionally opened under boundary load, thus the propagation of elastic wave is suppressed effectively. The study provides a new idea to design perforated-panel metamaterial.

Key words: boundary load, hierarchy, elliptical perforated-panel, metamaterial, finite element method, bandgap

CLC Number:

O328

ZHANG Zujian, GUO Hui, WANG Xiaowei, YUAN Tao, SUN Pei. Effect of Boundary Load on Bandgaps of Elliptical Perforated-Hierarchical Panel Metamaterials[J]. Journal of Synthetic Crystals, 2023, 52(2): 261-270.

References

[1] HONG C, ELLIOTT S J. Local feedback control of light honeycomb panels[J]. The Journal of the Acoustical Society of America, 2007, 121(1): 222-233.
[2] 徐俭乐, 崔洪宇, 洪明. 声子晶体夹层板结构的隔声性能研究[J]. 振动与冲击, 2021, 40(9): 285-291.
XU J L, CUI H Y, HONG M. Sound insulation performance of phononic crystal sandwich plate structure[J]. Journal of Vibration and Shock, 2021, 40(9): 285-291(in Chinese).
[3] LIU A P, ZHOU X M, HUANG G L, et al. Super-resolution imaging by resonant tunneling in anisotropic acoustic metamaterials[J]. The Journal of the Acoustical Society of America, 2012, 132(4): 2800-2806.
[4] MA G C, YANG M, YANG Z Y, et al. Low-frequency narrow-band acoustic filter with large orifice[J]. Applied Physics Letters, 2013, 103(1): 011903.
[5] YANG P, WU J Z, ZHAO R R, et al. Study of high frequency acoustic directional transmission model based on graphene structure[J]. AIP Advances, 2020, 10(3): 035308.
[6] MALDOVAN M. Sound and heat revolutions in phononics[J]. Nature, 2013, 503(7475): 209-217.
[7] ACHAOUI Y, KHELIF A, BENCHABANE S, et al. Experimental observation of locally-resonant and Bragg band gaps for surface guided waves in a phononic crystal of Pillars[J]. Physical Review B, 2011, 83(10): 104201.
[8] LIU Z, ZHANG X, MAO Y, et al. Locally resonant sonic materials[J]. Science, 2000, 289(5485): 1734-1736.
[9] YAO Z C, ZHAO R X, ZEGA V, et al. A metaplate for complete 3D vibration isolation[J]. European Journal of Mechanics-A/Solids, 2020, 84: 104016.
[10] WANG Y F, WANG Y S. Multiple wide complete bandgaps of two-dimensional phononic crystal slabs with cross-like holes[J]. Journal of Sound and Vibration, 2013, 332(8): 2019-2037.
[11] WANG Y F, WANG Y S, SU X X. Large bandgaps of two-dimensional phononic crystals with cross-like holes[J]. Journal of Applied Physics, 2011, 110(11): 113520.
[12] KRUSHYNSKA A O, MINIACI M, BOSIA F, et al. Coupling local resonance with Bragg band gaps in single-phase mechanical metamaterials[J]. Extreme Mechanics Letters, 2017, 12: 30-36.
[13] TIAN X Y, CHEN W J, GAO R J, et al. Merging Bragg and local resonance bandgaps in perforated elastic metamaterials with embedded spiral holes[J]. Journal of Sound and Vibration, 2021, 500: 116036.
[14] CHENG Q, GUO H, YUAN T, et al. Topological design of square lattice structure for broad and multiple band gaps in low-frequency range[J]. Extreme Mechanics Letters, 2020, 35: 100632.
[15] SUN P, ZHANG Z D, GUO H, et al. Topological optimization of hierarchical honeycomb acoustic metamaterials for low-frequency extreme broad band gaps[J]. Applied Acoustics, 2022, 188: 108579.
[16] SEPEHRI S, JAFARI H, MASHHADI M M, et al. Study of tunable locally resonant metamaterials: effects of spider-web and snowflake hierarchies[J]. International Journal of Solids and Structures, 2020, 204/205: 81-95.
[17] MINIACI M, KRUSHYNSKA A, GLIOZZI A S, et al. Design and fabrication of bioinspired hierarchical dissipative elastic metamaterials[J]. Physical Review Applied, 2018, 10(2): 024012.
[18] BILLON K, ZAMPETAKIS I, SCARPA F, et al. Mechanics and band gaps in hierarchical auxetic rectangular perforated composite metamaterials[J]. Composite Structures, 2017, 160: 1042-1050.
[19] XU X C, BARNHART M V, LI X P, et al. Tailoring vibration suppression bands with hierarchical metamaterials containing local resonators[J]. Journal of Sound and Vibration, 2019, 442: 237-248.
[20] BERTOLDI K, BOYCE M C, DESCHANEL S, et al. Mechanics of deformation-triggered pattern transformations and superelastic behavior in periodic elastomeric structures[J]. Journal of the Mechanics and Physics of Solids, 2008, 56(8): 2642-2668.
[21] BERTOLDI K, BOYCE M C. Mechanically triggered transformations of phononic band gaps in periodic elastomeric structures[J]. Physical Review B, 2008, 77(5): 052105.
[22] BOATTI E, VASIOS N, BERTOLDI K. Origami metamaterials for tunable thermal expansion[J]. Advanced Materials, 2017, 29(26): 1700360.
[23] SHIM J, WANG P, BERTOLDI K. Harnessing instability-induced pattern transformation to design tunable phononic crystals[J]. International Journal of Solids and Structures, 2015, 58: 52-61.
[24] GAO N, LI J, BAO R H, et al. Harnessing uniaxial tension to tune Poisson’s ratio and wave propagation in soft porous phononic crystals: an experimental study[J]. Soft Matter, 2019, 15(14): 2921-2927.
[25] GRIMA J N, MIZZI L, AZZOPARDI K M, et al. Auxetic perforated mechanical metamaterials with randomly oriented cuts[J]. Advanced Materials, 2016, 28(2): 385-389.
[26] JAVID F, WANG P, SHANIAN A L, et al. Architected materials with ultra-low porosity for vibration control[J]. Advanced Materials, 2016, 28(28): 5943-5948.
[27] TIAN X Y, CHEN W J, GAO R J, et al. Perforation-rotation based approach for band gap creation and enlargement in low porosity architected materials[J]. Composite Structures, 2020, 245: 112331.
[28] TRAINITI G, RIMOLI J J, RUZZENE M. Wave propagation in undulated structural lattices[J]. International Journal of Solids and Structures, 2016, 97/98: 431-444.
[29] FOEHR A, BILAL O R, HUBER S D, et al. Spiral-based phononic plates: from wave beaming to topological insulators[J]. Physical Review Letters, 2018, 120(20): 205501.
[30] NING S W, YANG F Y, LUO C C, et al. Low-frequency tunable locally resonant band gaps in acoustic metamaterials through large deformation[J]. Extreme Mechanics Letters, 2020, 35: 100623.
[31] LI J, WANG Y T, CHEN W Q, et al. Harnessing inclusions to tune post-buckling deformation and bandgaps of soft porous periodic structures[J]. Journal of Sound and Vibration, 2019, 459: 114848.
[32] DUDEK K K, MARTÍNEZ J A I, ULLIAC G, et al. Micro-scale auxetic hierarchical mechanical metamaterials for shape morphing[J]. Advanced Materials, 2022, 34(14): e2110115.
[33] SHI H Y Y, TAY T E, LEE H P. Elastic wave propagation in perforated plates with tetrad elliptical structural hierarchy: numerical analysis and experimental verification[J]. Journal of Sound and Vibration, 2019, 448: 73-82.
[34] JIN W C, GUO H, SUN P, et al. Numerical investigation of discrepancies between two-dimensional and three-dimensional acoustic metamaterials[J]. Frontiers in Materials, 2021, 8: 759740.