Phononic crystals are composite materials consisting of periodically distributed inclusions, and this structure enables wave band gaps under specific conditions. This characteristic allows for the suppression of elastic waves within certain frequency ranges, offering a new approach to vibration reduction and noise control. In this study, phononic crystals, with their periodic structure, tunable bandgap properties, topology optimization, and additive manufacturing technology, are reviewed. Some key hot issues, such as low-frequency vibration and noise control, intelligent materials, and tunable bandgap design, are discussed. In the future, phononic crystals will play a significant role in barrier vibration isolation, rail transit vibration isolation, power equipment vibration isolation, precision equipment vibration isolation, noise control, and underground protection engineering. This study constitutes a systematic summary and outlook of phononic crystals in modern engineering vibration and noise control.
TammI. Über die Quantentheorie der molekularen Lichtzerstreuung in festen Körpern. Z Phys1930; 60: 345–363.
3.
ZimanJM. Electrons and phonons: the theory of transport phenomena in solids. Oxford: OUP, 2001.
4.
MaldovanM. Sound and heat revolutions in phononics. Nature2013; 503: 209–217.
5.
LandauLDPitaevskiiLPKosevichAM, et al.Theory of elasticity. (3rd ed.) Butterworth-Heinemann, 2012.
6.
AuldBA. Acoustic fields and waves in solids. (2nd ed.) R. E. Krieger, 1990.
7.
DeymierPA. Acoustic metamaterials and phononic crystals. Springer Science & Business Media, 2013.
8.
SledzinskaMGraczykowskiBMaireJ, et al.2D phononic crystals: progress and prospects in hypersound and Thermal transport engineering. Adv Funct Mater2020; 30: 1904434.
9.
KhelifAAdibiA. Phononic crystals: fundamentals and applications. Springer, 2016.
10.
LaudeV. Phononic crystals: artificial crystals for sonic, acoustic, and elastic waves, de gruyter studies in mathematical physics No. Vol. 26. De Gruyter, 2015.
11.
Romero-GarciaVHladky-HennionAC. Fundamentals and applications of acoustic metamaterials: from seismic to radio frequency. Wiley, 2019.
12.
PennecYVasseurJODjafari-RouhaniB, et al.Two-dimensional phononic crystals: Examples and applications. Surf Sci Rep2010; 65: 229–291.
13.
WarmuthFWormserMKörnerC. Single phase 3D phononic band gap material. Sci Rep2017; 7: 3843.
14.
LucklumFVellekoopMJ. Bandgap engineering of three-dimensional phononic crystals in a simple cubic lattice. Appl Phys Lett2018; 113: 201902.
15.
Aravantinos-ZafirisNLucklumFSigalasMM. Complete phononic band gaps in the 3D Yablonovite structure with spheres. Ultrasonics2021; 110: 106265.
16.
SigalasMMEconomouEN. Elastic and acoustic wave band structure. J Sound Vib1992; 158: 377–382.
17.
KushwahaMSHaleviPDobrzynskiL, et al.Acoustic band structure of periodic elastic composites. Phys Rev Lett1993; 71: 2022–2025.
18.
SimonsDA. Reflection of Rayleigh waves by strips, grooves, and periodic arrays of strips or grooves. J Acoust Soc Am1978; 63: 1292–1301.
19.
GlassNELoudonRMaradudinAA. Propagation of Rayleigh surface waves across a large-amplitude grating. Phys Rev B1981; 24: 6843–6861.
20.
SeshadriSR. Effect of periodic surface corrugation on the propagation of Rayleigh waves. J Acoust Soc Am1979; 65: 687–694.
Martinez-SalaRSanchoJSanchezJV, et al.Sound attenuation by sculpture. Nature1995; 378(6554): 241.
23.
amesRWoodleySMDyerCM. Sonic bands, bandgaps, and defect states in layered structures: theory and experiment. J Acoust Soc Am1995; 97(4): 2041–2047.
24.
KushwahaMSDjafari-RouhaniBDobrzynskiL. Sound isolation from cubic arrays of air bubbles in water. Phys Lett1998; 248(2): 252–256.
25.
WenXWenJ. Yu dianlong 2009 phononic crystal. Beijing: National Defense Industry Press.
26.
SchevenelsMLombaertG. Double wall barriers for the reduction of ground vibration transmission. Soil Dynam Earthq Eng2017; 97: 1–13.
27.
ConnollyDGiannopoulosAFanW, et al.Optimising low acoustic impedance back-fill material wave barrier dimensions to shield structures from ground borne high speed rail vibrations. Constr Build Mater2013; 44: 557–564.
28.
SigalasMMEconomouEN. Elastic and acoustic wave band structure. J Sound Vib1992; 158(2): 377–382.
29.
KushwahaMSHaleviPDobrzynskiL, et al.Acoustic band structure of periodic elastic composites. Phys Rev Lett1993; 71(13): 2022–2025.
30.
PanahiEHosseinkhaniAKhansanamiMF, et al.Novel cross shape phononic crystals with broadband vibration wave attenuation characteristic: design, modeling and testing. Thin-Walled Struct2021; 163: 107665.
31.
HuangYLiJChenW, et al.Tunable bandgaps in soft phononic plates with spring-mass-like resonators. Int J Mech Sci2019; 151: 300–313.
32.
LiuZZhangXMaoY, et al.Locally resonant sonic materials. Science2000; 289(5485): 1734–1736.
33.
YuDL. Research on the vibration band gaps of periodic beams and plates based on the theory of phononic crystals [D]. Changsha: National Defense Science and Technology, 2006.
34.
LiJChanCT. Double-negative acoustic metamaterial. Phys Rev E - Stat Nonlinear Soft Matter Phys2004; 70(5 Pt 2): 055602.
35.
LiuZZhangXMaoY, et al.Locally resonant sonic materials. Science2000; 289(5485): 1734–1736.
36.
RupinMLemoultFLeroseyG, et al.Experimental demonstration of ordered and disordered multiresonant metamaterials for lamb waves. Phys Rev Lett2014; 112(23): 234301. DOI: 10.1103/PhysRevLett.112.234301.
37.
WilliamsEGRouxPRupinM, et al.Theory of multiresonant metamaterials forA0Lamb waves. Phys Rev B2015; 91(10): 104307. DOI: 10.1103/PhysRevB.91.104307.
38.
CelliPYousefzadehBDaraioC, et al.Bandgap widening by disorder in rainbow metamaterials. Appl Phys Lett2019; 114(9): 091903. DOI: 10.1063/1.5081916.
39.
LiuLHusseinMI. Wave motion in periodic flexural beams and characterization of the transition between bragg scattering and local resonance. J Appl Mech2012; 79(1): 011003. DOI: 10.1115/1.4004592.
40.
KrushynskaAOMiniaciMBosiaF, et al.Coupling local resonance with Bragg band gaps in single-phase mechanical metamaterials. Extreme Mech Lett2017; 12: 30–36. DOI: 10.1016/j.eml.2016.10.004.
41.
ChuangK-CLvX-FWangYH. A bandgap switchable elastic metamaterial using shape memory alloys. J Appl Phys2019; 125(5): 055101. DOI: 10.1063/1.5065557.
42.
NaifyCJChangCMMcKnightG, et al.Scaling of membrane-type locally resonant acoustic metamaterial arrays. J Acoust Soc Am2012; 132(4): 2784–2792. DOI: 10.1121/1.4744941.
43.
BarnhartMVXuXCChenYY, et al.Experimental demonstration of a dissipative multi-resonator metamaterial for broadband elastic wave attenuation. J Sound Vib2019; 438: 1–12. DOI: 10.1016/j.jsv.2018.08.035.
44.
ChenYYBarnhartMVChenJK, et al.Dissipative elastic metamaterials for broadband wave mitigation at subwavelength scale. Compos Struct2016; 136: 358–371. DOI: 10.1016/j.compstruct.2015.09.048.
45.
ZhuJChristensenJJungJ, et al.A holey-structured metamaterial for acoustic deep-subwavelength imaging. Nat Phys2010; 7: 52–55. DOI: 10.1038/nphys1804.
46.
ZhangZChengYLiuX, et al.Subwavelength multiple topological interface states in one-dimensional labyrinthine acoustic metamaterials. Phys Rev B2019; 99(22): 224104. DOI: 10.1103/PhysRevB.99.224104.
47.
ZhangZGuYLongH, et al.Subwavelength acoustic valley-hall topological insulators using soda cans honeycomb lattices. Research2019; 2019: 5385763. DOI: 10.34133/2019/5385763.
48.
ChengZBShiZF. Composite periodic foundation and its application for seismic isolation. Earthq Eng Struct Dynam2018; 47(4): 925–944. DOI: 10.1002/eqe.2999.
49.
CasablancaOVenturaGGaresciF, et al.Seismic isolation of buildings using composite foundations based on metamaterials. J Appl Phys2018; 123. DOI: 10.1063/1.5018005.
50.
MuhammadLCWLimC. Elastic waves propagation in thin plate metamaterials and evidence of low frequency pseudo and local resonance bandgaps. Phys Lett2019; 383(23): 2789–2796. DOI: 10.1016/j.physleta.2019.05.039.
51.
MuhammadLCWLimCWReddyJ. Built-up structural steel sections as seismic metamaterials for surface wave attenuation with low frequency wide bandgap in layered soil medium. Eng Struct2019; 188: 440–451. DOI: 10.1016/j.engstruct.2019.03.046.
52.
GraczykowskiB. Progress and perspectives on phononic crystals. J Appl Phys2021; 129: 160901.
53.
PennecYVasseurJODjafari-RouhaniB, et al.Two-dimensional phononic crystals: Examples and applications. Surf Sci Rep2010; 65(8): 229–291.
54.
WangKZhouJXuD, et al.Lower band gaps of longitudinal wave in a one-dimensional periodic rod by exploiting geometrical nonlinearity. Mech Syst Signal Process2019; 124: 664–678.
55.
LiJFanXLiF. Numerical and experimental study of a sandwich-like metamaterial plate for vibration suppression. Compos Struct2020; 238: 111969.
56.
ZhouJDouLWangK, et al.A nonlinear resonator with inertial amplification for very low-frequency flexural wave attenuations in beams. Nonlinear Dyn2019; 96: 647–665.
57.
ElmadihWChronopoulosDSyamWP, et al.Three-dimensional resonating metamaterials for low-frequency vibration attenuation. Sci Rep2019; 9(1): 11503.
58.
WangG. Research on phononic crystal local resonance band gap mechanism and vibration characteristics[D]. Changsha: Doctoral Dissertation of National Defense Science and Technology, 2006.
59.
WangGWenXWenJ, et al.Two-dimensional locally resonant phononic crystals with binary structures. Phys Rev Lett2004; 93(15): 154302.
60.
GangWYao-ZongLJi-HongW, et al.Formation mechanism of the low-frequency locally resonant band gap in the two-dimensional ternary phononic crystals. Chin Phys2006; 15(2): 407–411.
61.
SigalasMMEconomouEN. Attenuation of multiple-scattered sound. Europhys Lett1996; 36(4): 241–246.
62.
ShengPZhangXXLiuZ, et al.Locally resonant sonic materials. Phys B Condens Matter2003; 338(1-4): 201–205.
63.
WangGWenJHHanXY, et al.Finite difference time domain method for the study of band gap in two-dimensional phononic crystals. Acta Phys Sin2003; 52(8): 1943–1947.
64.
CaseIS. An efficient finite element method for computing spectra of photonic and acoustic band-gap materials. J Comput Phys1999; 150: 468–481.
65.
LangletPHladky-HennionACDecarpignyJN. Analysis of the propagation of plane acoustic waves in passive periodic materials using the finite element method. J Acoust Soc Am1995; 98(5): 2792–2800.
66.
Van KempenEBabischW. The quantitative relationship between road traffic noise and hypertension: a meta-analysis. J Hypertens2012; 30(6): 1075–1086.
67.
StansfeldSAMathesonMP. Noise pollution: non-auditory effects on health. Br Med Bull2003; 68(1): 243–257.
68.
YangBGuoKSunJ. Chatter detection in robotic milling using entropy features. Appl Sci2022; 12(16): 8276.
69.
PersingerMA. Infrasound, human health, and adaptation: an integrative overview of recondite hazards in a complex environment. Nat Hazards2014; 70(1): 501–525.
70.
RoundyS. On the effectiveness of vibration-based energy harvesting. J Intell Mater Syst Struct2005; 16(10): 809–823.
71.
LiuBFengTWuX, et al.ODS&Low-frequency noise analysis on the tilt open drum washing machine. Noise and Vibration Control2010; 30(3): 50–54.
72.
KangTFSunXWSongT, et al.Low-frequency band gap characteristics of two-dimensional hollow scatterer phonon crystal plate and its formation mechanism. Acta Acustica2020; 45(4): 601–608.
73.
VasileiadisTVargheseJBabacicV, et al. Progress and perspectives on phononic crystals. J Appl Phys2021; 129(16): 160901‐1–160901‐16.
74.
FujiiGTakahashiMAkimotoY. Acoustic cloak designed by topology optimization for acoustic–elastic coupled systems. Appl Phys Lett2021; 118(10): 101102‐1–101102‐5.
75.
HackettLMillerMBrimigionF, et al.Towards single-chip radiofrequency signal processing via acoustoelectric electron–phonon interactions. Nat Commun2021; 12(1): 2769.
76.
MaldovanM. Sound and heat revolutions in phononics. Nature2013; 503(7475): 209–217.
77.
NashLMKlecknerDReadA, et al.Topological mechanics of gyroscopic metamaterials. Proc Natl Acad Sci U S A2015; 112(47): 14495–14500.
78.
WeiZLiBDuJ, et al.Research on the vibration band gaps of isolators applied to ship hydraulic pipe supports based on the theory of phononic crystals. Eur Phys J Appl Phys2016; 74(1): 10902.
79.
LiHPCaoXXShiGT, et al.Research on sound insulation of floor support layer of high-speed trains based on phonon crystal. Noise and vibration control2024; 44(1): 220–225.
80.
ZhangJDengYPengZB, et al.Vibration reduction characteristics of ship engine based on phononic crystal. J Chongqing Jianzhu Univ2020; 39(9): 140–145.
81.
GuoXCuiHYHongM. Research on vibration and noise reduction of local resonant phononic crystal plate. J Ship Mech2021; 25(4): 509–516.
82.
ShenHJLiYFSuYS, et al.Review of sound and vibration control techniques for ship piping systems and exploration of photonic crystals applied in noise and vibration reduction. J Vib Shock2017; 36(15): 509–516.
83.
MaCRShaoCWanQM, et al.A locally-resonant phononic crystal for low-frequency vibration control of vehicles. Journal of applied acoustics2018; 37(1): 152–158.
84.
ZuoSGTanQWSunQ, et al.Vibration reduction with phononic crystals beams for subframe of a fuel-cell car. Journal of shock and vibration2013; 32(18): 26–30.
85.
ZhangJLYaoHDuJ, et al.Low frequency sound insulation characteristics of the locally resonant phononic crystals in the large aircraft cabin. J Chin Ceram Soc2016; 44(10): 1440–1445.
86.
ZhangJShenWMQianDH. Vibration reduction characteristics of offshore wind turbines based on locally resonant phononic crystal tower structure. Noise and vibration control2024; 44(1): 1–6.
87.
AlbinoCGodinhoLAmado-MendesP, et al.3D FEM analysis of the effect of buried phononic crystal barriers on vibration mitigation. Eng Struct2019; 196: 109340.
88.
MiaoLLeiLLiC, et al.Vibration reduction of phononic-like crystal metaconcrete track bed for underground railway. J Mater Civ Eng2023; 35(8): 04023254.
89.
KushwahaMS. Stop-bands for periodic metallic rods: sculptures that can filter the noise. Appl Phys Lett1997; 70(24): 3218–3220.
90.
Martínez-SalaRRubioCGarcía-RaffiLM, et al.Control of noise by trees arranged like sonic crystals. J Sound Vib2006; 291(1–2): 100–106.
91.
XiaoYWenJYuD, et al.Flexural wave propagation in beams with periodically attached vibration absorbers: band-gap behavior and band formation mechanisms. J Sound Vib2013; 332(4): 867–893.
92.
XiaoYWenJWenX. Longitudinal wave band gaps in metamaterial-based elastic rods containing multi-degree-of-freedom resonators. New J Phys2012; 14(3): 033042–33061.
93.
XiaoYMaceBRWenJ, et al.Formation and coupling of band gaps in a locally resonant elastic system comprising a string with attached resonators. Phys Lett2011; 375(12): 1485–1491.
94.
YuDWenJZhaoH, et al.Flexural vibration band gap in a periodic fluid-conveying pipe system based on the timoshenko beam theory. J Vib Acoust2011; 133: 0145021.
95.
WangJWangGWenJ, et al.Flexural vibration band gaps in periodic stiffened plate structures. Mech2012; 18(2): 186–191.
96.
YangZMeiJYangM, et al.Membrane-type acoustic metamaterial with negative dynamic mass. Phys Rev Lett2008; 101(20): 204301.
97.
MirandaEJPNobregaEDRodriguesSF, et al.Wave attenuation in elastic metamaterial thick plates: analytical, numerical and experimental investigations. Int J Solid Struct2020; 204: 138–152.
98.
De MiguelAGCinefraMFilippiM, et al.Validation of FEM models based on Carrera Unified Formulation for the parametric characterization of composite metamaterials[J]. J Sound Vib2021; 498: 115979.
99.
OudichMLiYAssouarBM, et al.A sonic band gap based on the locally resonant phononic plates with stubs. New J Phys2010; 12(8): 083049.
100.
JinYFernezNPennecY, et al.Tunable waveguide and cavity in a phononic crystal plate by controlling whispering-gallery modes in hollow pillars. Phys Rev B2016; 93(5): 054109.
101.
ZhuHFSunXWSongT, et al.Tunable characteristics of low-frequency bandgaps in two-dimensional multivibrator phononic crystal plates under Prestrain. Sci Rep2021; 11(1): 8389.
102.
ZhangSBLiuJZhangHB, et al.Tunable low frequency band gap and waveguide of phononic crystal plates with different filling ratio. Crystals2021; 11(7): 828.
103.
KrushynskaAOMiniaciMBosiaF, et al.Coupling local resonance with Bragg band gaps in single-phase mechanical metamaterials. Extreme Mechanics Letters2017; 12: 30–36.
104.
ZhouXLXuYLLiuY, et al.Extending and lowering band gaps by multilayered locally resonant phononic crystals. Appl Acoust2018; 133: 97–106.
105.
LiYZhouQZhuL, et al.Hybrid radial plate-type elastic metamaterials for lowering and widening acoustic bandgaps. Int J Mod Phys B2018; 32: 1850286.
106.
GuoJCLiJRZhangZ. Interface design of low-frequency band gap characteristics in stepped hybrid phononic crystals. Appl Acoust2021; 182: 108209.
107.
GuptaVMunianRKBhattacharyaB. Dispersion analysis of the hourglass-shaped periodic shell lattice structure. Int J Solid Struct2022; 254–255: 111931.
108.
MaXLiZXiangJ, et al.Optimization of a ring-like phononic crystal structure with bonding layers for band gap. Mech Syst Signal Process2022; 173: 109059.
109.
FanLGeHZhangS-Y, et al.Nonlinear acoustic fields in acoustic metamaterial based on a cylindrical pipe with periodically arranged side holes. J Acoust Soc Am2013; 133: 3846–3852.
110.
FanLChenZDengYC, et al.Nonlinear effects in a metamaterial with double negativity. Appl Phys Lett2014; 105: 041904.
111.
ChenZXueCFanL, et al.A tunable acoustic metamaterial with double-negativity driven by electromagnets. Sci Rep2016; 6: 30254.
112.
LeeKJBJungMKLeeSH. Highly tunable acoustic metamaterials based on a resonant tubular array. Phys Rev B2012; 86: 184302.
113.
WangPCasadeiFShanS, et al.Harnessing buckling to design tunable locally resonant acoustic metamaterials. Phys Rev Lett2014; 113: 014301.
114.
ParkJJLeeKJBWrightOB, et al.Giant acoustic concentration by extraordinary transmission in zero-mass metamaterials. Phys Rev Lett2013; 110: 244302.
115.
JinYPennecYPanY, et al.Phononic crystal plate with hollow pillars actively controlled by fluid filling. Crystals2016; 6: 64.
WenJShenHYuD, et al.Exploration of amphoteric and negative refraction imaging of acoustic sources via active metamaterials. Phys Lett2013; 377: 2199–2206.
118.
PopaB-IZigoneanuLCummerSA. Tunable active acoustic metamaterials. Phys Rev B2013; 88: 024303.
119.
XiaoSMaGLiY, et al.Active control of membranetype acoustic metamaterial by electric field. Appl Phys Lett2015; 106: 091904.
120.
MaGFanXShengP, et al.Shaping reverberating sound fields with an actively tunable metasurface. Proc Natl Acad Sci U S A2018; 115: 6638–6643.
121.
ChenXXuXAiS, et al.Active acoustic metamaterials with tunable effective mass density by gradient magnetic fields. Appl Phys Lett2014; 105: 071913.
122.
BabaeeSOverveldeJTBChenER, et al.Reconfigurable origami-inspired acoustic waveguides. Sci Adv2016; 2: e1601019.
123.
BückmannTThielMKadicM, et al.An elastomechanical unfeelability cloak made of pentamode metamaterials. Nat Commun2014; 5: 4130.
ChangTJeonSHeoM, et al.Mimicking bio-mechanical principles in photonic metamaterials for giant broadband nonlinearity. Commun Phys2020; 3: 79.
126.
ZhuSTanXWangB, et al.Bio-inspired multistable metamaterials with reusable large deformation and ultra-high mechanical performance. Extreme Mech Lett2019; 32: 100548.
127.
KadicMBückmannTStengerN, et al.On the practicability of pentamode mechanical metamaterials. Appl Phys Lett2012; 100: 191901.
BayatAGordaninejadF. Band-gap of a soft magnetorheological phononic crystal. J Vib Acoust2015; 137(1): 011011.
130.
WuBHeCWeiR, et al.Research on two-dimensional phononic crystal with magnetorheological material[C]//2008 IEEE Ultrasonics Symposium. IEEE, 2008, pp. 1484–1486.
131.
OzerZ. Dispersion features of elastic waves in phononic crystals: finite element analysis. Ferroelectrics2019; 544(1): 68–74.
132.
LiaoTSunXSongT, et al.Tunable bandgaps in novel two-dimensional piezoelectric phononic crystal slab[J]. Acta Phys Sin2018; 67: 21420821.
133.
VasseurJHladky-HennionACDeymierP, et al.Waveguiding in supported phononic crystal plates. J Phys : Conf Ser2007; 92(1): 012111.
134.
XuCW. The temperature tunable phonoic crystal based on ferroelectric ceramic barium strontium titanate. Xiangtan. Xiangtan university, 2015.
135.
ZhangGGaoY. Tunability of band gaps in two-dimensional phononic crystals with magnetorheological and electrorheological composites. Acta Mech Solida Sin2021; 34(1): 40–52.
136.
YehJ. Control analysis of the tunable phononic crystal with electrorheological material. Phys B Condens Matter2007; 400(1–2): 137–144.
137.
SongYShenY. A tunable phononic crystal system for elastic ultrasonic wave control. Appl Phys Lett2021; 118: 22410422.
138.
JangJKohCYBertoldiK, et al.Combining pattern instability and shape-memory hysteresis for phononic switching. Nano Lett2009; 9(5): 2113–2119.
139.
ZhangXKangZ. Topology optimization of magnetorheological fluid layers in sandwich plates for semi-active vibration control. Smart Mater Struct2015; 24: 085024.
140.
ShakeriADarbariSMoravvej-FarshiMK. Designing a tunable acoustic resonator based on defect modes, stimulated by selectively biased PZT rods in a 2D phononic crystal. Ultrasonics2019; 92: 8–12.
141.
ZhangXYeHWeiN, et al.Design optimization of multifunctional metamaterials with tunable thermal expansion and phononic bandgap. Mater Des2021; 209: 109990.
142.
CasadeiFDelperoTBergaminiA, et al. Piezoelectric resonator arrays for tunable acoustic waveguides and metamaterials. J Appl Phys2012; 112(6): 141–143.
143.
WangTTWangYFDengZC, et al.Reconfigurable waveguides defined by selective fluid filling in two-dimensional phononic metaplates. Mech Syst Signal Process2022; 165: 108392.
144.
WangTTWangYFWangYS, et al. Tunable fluid-filled phononic metastrip. Appl Phys Lett. 2017; 111(4): 041906‐1–041906‐4.
145.
WangTTWangYFDengZC, et al.Reconfigurable coupled-resonator acoustoelastic waveguides in fluid-filled phononic metaplates. Compos Struct2023; 303: 116355.
146.
ZhangQChenYZhangK, et al.Programmable elastic valley Hall insulator with tunable interface propagation routes. Extreme Mechanics Letters2019; 28: 76–80.
147.
YanWGaoY.Tunable acoustic waveguide based on a magnetorhcological fluid filling. APEX2021; 14(1): 16501.
148.
YangBGuoKSunJ. Towards metamaterial rods with amplitude-dependent band gaps:A superelastic alloy-based approach. Mech Syst Signal Process2022; 166: 108459.
149.
ZhangSShiYGaoY. Tunability of band structures in a two-dimensional magnetostrictive phononic crystal plate with stress and magnetic loadings. Phys Lett2017; 381(12): 1055–1066.
150.
QianDZouPZhangJ, et al.Tunability of resonator with pre-compressed springs on thermo-magneto-mechanical coupling band gaps of locally resonant phononic crystal nanobeam with surface effects. Mech Syst Signal Process2022; 176: 109184.
151.
WangZZhangQZhangK, et al.Tunable digital metamaterial for broadband vibration isolation at low frequency. Adv Mater2016; 28(44): 9857–9861.
152.
GuoTLiBZhangS, et al. Using eddy-current vibration absorbers to design locally resonant periodic structures. J Appl Phys2019; 125(23): 235103‐1–235103‐10.
153.
LiJYangPLiS. Phononic band gaps by inertial amplification mechanisms in periodic composite sandwich beam with lattice truss cores. Compos Struct2020; 231: 111458.
154.
LuQWangPLiuC. An analytical and experimental study on adaptive active vibration control of sandwich beam. Int J Mech Sci2022; 232: 107634.
155.
ZhongHLWuFGYaoLN. Application of genetic algorithm in optimization of band gap of two-dimensional phononic crystals. ACTA Physica sinica2006; 55(1): 275–280.
156.
Yao-HeLYuanCJian-MinX. Band gap optimization in phononic crystals based on intelligence algorithm. J Vib Shock2008; 27(9): 94–96.
157.
ChiaCMRongongJAWordenK. Strategies for using cellular automata to locate constrained layer damping on vibrating structures. J Sound Vib2009; 319: 119–139.
158.
SigmundOJensenJS. Philosophical transactions of the royal society A. Phys Eng Sci2003; 361: 1001.
159.
LiuZZhuDRodriguesSP, et al.Generative model for the inverse design of metasurfaces. Nano Lett2018; 18: 6570–6576.
160.
LongYRenJLiY, et al.Inverse design of photonic topological state via machine learning. Appl Phys Lett2019; 114: 181105.
JinYHeLWenZ, et al.Intelligent on-demand design of phononic metamaterials. Nanophotonics2022; 11: 439–460.
163.
SigmundOJensenJS. Systematic design of phononic bandgap materials and structures by topology optimization. Philos Trans A Math Phys Eng Sci2003; 361: 1001–1019.
164.
VatanabeSLPaulinoGHSilvaECN. Maximizing phononic band gaps in piezocomposite materials by means of topology optimization. J Acoust Soc Am2014; 136: 494–501.
165.
WormserMWeinFStinglM, et al.Design and additive manufacturing of 3D phononic band gap structures based on gradient based optimization. Materials2017; 10(10): 1125.
166.
LiangXToACDuJ, et al.Topology optimization of phononic-like structures using experimental material interpolation model for additive manufactured lattice infills. Comput Methods Appl Mech Eng2021; 377: 113717.
167.
HedayatrasaSAbharyKUddinMS, et al.Optimal design of tunable phononic bandgap plates under equibiaxial stretch. Smart Mater Struct2016; 25: 055025.
168.
BortotEAmirOShmuelG. Topology optimization of dielectric elastomers for wide tunable band gaps. Int J Solid Struct2018; 143: 262–273.
169.
DongHWSuXXWangYS, et al.Topological optimization of two-dimensional phononic crystals based on the finite element method and genetic algorithm. Struct Multidiscip Optim2014; 50: 593–604.
170.
KimMGHashimotoHAbeK, et al.Level set based topological shape optimization of phononic crystals. JCOSEIK2012; 25(6): 549–558.
171.
LiuGR. A generalized gradient smoothing technique and the smoothed bilinear form for Galerkin formulation of a wide class of computational methods. Int J Comput Methods2008; 05(02): 199–236.
172.
LiuGR. A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part I theory. Int J Numer Methods Eng2010; 81(9): 1093–1126.
173.
A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part II applications to solid mechanics problems. Int J Numer Methods Eng2010; 81(9): 1127–1156.
174.
LiuGR. The smoothed finite element method (S-FEM): a framework for the design of numerical models for desired solutions. Front Struct Civ Eng2019; 13: 456–477.
175.
KharatVJSinghPRajuGS, et al.Additive manufacturing (3D printing): a review of materials, methods, applications and challenges. Mater Today Proc2023.
176.
HashemiSMParviziSBaghbanijavidH, et al.Computational modelling of process-structure-property-performance relationships in metal additive manufacturing: a review. Int Mater Rev2022; 67(1): 1–46. DOI: 10.1080/09506608.2020.1868889.
177.
NgoTDKashaniAImbalzanoG, et al. Additive manufacturing (3D printing): a review of materials, methods, applications and challenges. Composites Part B: Engineering2018; 143: 172–196.
178.
KoernerC. Additive manufacturing of metallic components by selective electron beam melting - a review. Int Mater Rev2016; 61: 361–377.
179.
GuDDMeinersWWissenbachK, et al.Laser additive manufacturing of metallic components: materials, processes and mechanisms. Int Mater Rev2012; 57: 133–164.
180.
GuDDShiXYPopraweR, et al.Material-structure-performance integrated laser-metal additive manufacturing. Science2021; 372: eabg1487.
181.
MosallanejadMHNiroumandBAversaA, et al.In-situ alloying in laser-based additive manufacturing processes: a critical review. J Alloys Compd2021; 872: 159567.
182.
PadhyGKWuCSGaoS. Friction stir based welding and processing technologies - processes, parameters, microstructures and applications: a review. J Mater Sci Technol2018; 34: 1–38.
183.
LiWYYangKYinS, et al.Solidstate additive manufacturing and repairing by cold spraying: a review. J Mater Sci Technol2018; 34: 440–457.
184.
Gonzalez-GutierrezJCanoSSchuschniggS, et al.Additive manufacturing of metallic and ceramic components by the material extrusion of highly-filled polymers: a review and future perspectives. Materials2018; 11: 840.
185.
YuHZMishraRS. Additive friction stir deposition: a deformation processing route to metal additive manufacturing. Materials Research Letters2021; 9: 71–83.
186.
TanZJLiJYZhangZ. Experimental and numerical studies on fabrication of nanoparticle reinforced aluminum matrix composites by friction stir additive manufacturing. J Mater Res Technol2021; 12: 1898–1912.
187.
ZhangZTanZJLiJY, et al.Experimental and numerical studies of re-stirring and re-heating effects on mechanical properties in friction stir additive manufacturing. Int J Adv Manuf Technol2019; 104: 767–784.
188.
ZhangZ. A review on additive manufacturing of wave controlling metamaterial. Int J Adv Manuf Technol2023; 124(3): 647–680.
189.
LuBHLiDC. Development of the additive manufacturing (3D) technology. Machine building & automation2013; 42(4): 1–4.
190.
Al-KetanOAbu Al-RubRK. Multifunctional mechanical metamaterials based on triply periodic minimal surface lattices. Adv Eng Mater2019; 21(10): 1900524.
191.
MaconachieTLearyMLozanovskiB, et al.SLM lattice structures: properties, performance, applications and challenges. Mater Des2019; 183: 108137.
192.
FengJFuJLinZ, et al.A review of the design methods of complex topology structures for 3D printing. Vis Comput Ind Biomed Art2018; 1: 5–16.
193.
TolSDegertekinFLErturkA. 3D-printed phononic crystal lens for elastic wave focusing and energy harvesting[J]. Addit Manuf2019; 29: 100780.
194.
AllamASabraKErturkA. Sound energy harvesting by leveraging a 3D-printed phononic crystal lens. Appl Phys Lett2021; 118(10): 103504.
195.
LiZYangSWangD, et al. Focus of ultrasonic underwater sound with 3D printed phononic crystal. Appl Phys Lett2021; 119(7): 073501.
IglesiasMJAMoughamesJUlliacG, et al. Three-dimensional phononic crystal with ultra-wide bandgap at megahertz frequencies. Appl Phys Lett2021; 118(6): 063507.
198.
ChoiCBansalSMünzenriederN, et al.Fabricating and assembling acoustic metamaterials and phononic crystals[J]. Advanced Engineering Materials2021; 23(2): 2000988.
199.
LiWCaoHZhangL, et al.Improved nonlinear ultrasound sensing based on 3D printing phonon crystals[C]2022 international conference on sensing, measurement & data analytics in the era of artificial intelligence (ICSMD). IEEE, 2022, pp. 1–5.
200.
LiWCaoHZhangL, et al.Nonlinear ultrasonic detection enhanced by 3-D printed phononic crystals. IEEE Trans Instrum Meas2023; 72: 1–8.
201.
SuarezLdel Mar EspinosaM. Assessment on the use of additive manufacturing technologies for acoustic applications. Int J Adv Manuf Technol2020; 109: 2691–2705.
202.
QureshiALiBTanKT. Numerical investigation of band gaps in 3D printed cantilever-in-mass metamaterials. Sci Rep2016; 6(1): 28314.
203.
McGeeOJiangHQianF, et al.3D printed architected hollow sphere foams with low-frequency phononic band gaps. Addit Manuf2019; 30: 100842.
204.
CaiZZhaoSHuangZ, et al.Bubble architectures for locally resonant acoustic metamaterials. Adv Funct Mater2019; 29(51): 1906984.
205.
HongYGuoKSunJ, et al. Investigation on vibration properties of 3D printed lattice structures filled with tin–bismuth alloy. J Appl Phys2022; 131(6): 131–134.
206.
WarmuthFWormserMKörnerC. Single phase 3D phononic band gap material. Sci Rep2017; 7(1): 3843.
207.
PengLMDengQCWuYJ, et al.Additive manufacturing of magnesium alloys by selective laser melting technology: a review. Acta Metall Sin2023; 59(1): 31–54.
208.
ZengZSalehiMKoppA, et al.Recent progress and perspectives in additive manufacturing of magnesium alloys. J Magnesium Alloys2022; 10(6): 1511–1541.
209.
EsmailyMZengZMortazaviAN, et al.A detailed microstructural and corrosion analysis of magnesium alloy WE43 manufactured by selective laser melting. Addit Manuf2020; 35: 101321.
210.
VasileiadisTVargheseJBabacicV, et al.Progress and perspectives on phononic crystals. J Appl Phys2021; 129: 16.
