This study investigates the flexural wave dispersion and bandgap mechanisms in bidirectional stiffened plates to quantify the influence of design parameters on bandgap properties and to support low-noise bridge design. A finite element model of the periodic unit cell is established, and a novel wavefield analysis based on a polarization ratio—defined as the proportion of out-of-plane displacement energy of the base plate—is proposed to identify flexural wave modes. Using this approach, dispersion characteristics and vibration transmission are computed, and bandgap formation mechanisms are clarified through eigenmode displacement fields. A parametric study assesses the effects of key design parameters on flexural wave bandgaps. Results show that the proposed method accurately identifies complex flexural wave modes. This research provides new insights and design references for source control of bridge structure-borne noise.
AltenKFleschR (2012) Finite element simulation prior to reconstruction of a steel railway bridge to reduce structure-borne noise. Engineering Structures35(2): 83–88. https://doi.org/10.1016/j.engstruct.2011.11.001
2.
ChengXSongXLiG (2025) Noise generation and contribution of a single-gap bridge expansion joint: an experimental and numerical study. Applied Acoustics229: 110387. https://doi.org/10.1016/j.apacoust.2024.110387
3.
ContrerasNZhangXHaoH, et al. (2024) Application of elastic metamaterials/meta-structures in civil engineering: a review. Composite Structures327: 117663. https://doi.org/10.1016/j.compstruct.2023.117663
4.
DongXChenKZhangJ, et al. (2024) Topological valley mode separation of elastic waves and potential applications. International Journal of Mechanical Sciences274: 109229. https://doi.org/10.1016/j.ijmecsci.2024.109229
5.
HusseinMILeamyMJRuzzeneM (2014) Dynamics of phononic materials and structures: historical origins, recent progress, and future outlook. Applied Mechanics Reviews66(4): 40802. https://doi.org/10.1115/1.4026911
6.
JeongYKimWLeeI, et al. (2019) Systematic experimental approach to determine banging noise source and location of a steel box girder using vibroacoustic analysis. Journal of Performance of Constructed Facilities33(3): 4019033. https://doi.org/10.1061/(asce)cf.1943-5509.0001287
7.
KnuthCSquicciariniGThompsonD (2023) An engineering approach for estimating the radiation efficiency of orthogonally stiffened plates. Journal of Vibration and Acoustics145(3): 31006. https://doi.org/10.1115/1.4056741
8.
LiYZhouQZhouL, et al. (2019) Flexural wave band gaps and vibration attenuation characteristics in periodic bi-directionally orthogonal stiffened plates. Ocean Engineering178: 95–103. https://doi.org/10.1016/j.oceaneng.2019.02.076
9.
LiR-SSunX-WTianJ-H, et al. (2024a) Broadband low-frequency sound insulation of a sandwich acoustic metamaterial with coupled-resonance. Journal of Applied Physics136(21): 213104. https://doi.org/10.1063/5.0227782
10.
LiXLiHJiangX, et al. (2024b) Experimental and numerical investigation on the vibro-acoustic characteristics of periodic rib stiffened plate based on band gap theory. Journal of Vibration and Control30(13–14): 3064–3076. https://doi.org/10.1177/10775463231188848
11.
LiangLLiXZhengJ, et al. (2020) Structure-borne noise from long-span steel truss cable-stayed bridge under damping pad floating slab: experimental and numerical analysis. Applied Acoustics157: 106988. https://doi.org/10.1016/j.apacoust.2019.07.036
12.
LiangLLiXSunY, et al. (2022) Measurement research on vibro-acoustic characteristics of large-span plate-truss composite bridge in urban rail transit. Applied Acoustics187: 108518. https://doi.org/10.1016/j.apacoust.2021.108518
13.
LinWTaniguchiNYodaT, et al. (2018) Renovation of existing steel railway bridges: field test and numerical simulation. Advances in Structural Engineering21(6): 809–823. https://doi.org/10.1177/1369433217732498
14.
LiuFShiPShenY, et al. (2024) Advances in suppression of structural vibration and sound radiation by flexural wave manipulation. Thin-Walled Structures200: 111936. https://doi.org/10.1016/j.tws.2024.111936
15.
LuoHCaoZYZhangX (2022) Combining different forms of statistical energy analysis to predict vibrations in a steel box girder comprising periodic stiffening ribs. Steel and Composite Structures45(1): 119–131.
16.
LuoHZhangXLuX, et al. (2024) Bandgap analysis of partial-interaction composite beams periodically attached vibration absorbers. International Journal of Mechanical Sciences267: 109006. https://doi.org/10.1016/j.ijmecsci.2024.109006
17.
MaTFanQLiZ, et al. (2020) Flexural wave energy harvesting by multi-mode elastic metamaterial cavities. Extreme Mechanics Letters41: 101073. https://doi.org/10.1016/j.eml.2020.101073
18.
MaZXuYShengX, et al. (2025) Research on the bandgap and flutter suppression of thin-film phononic crystals for satellite honeycomb panels. Thin-Walled Structures209: 112865. https://doi.org/10.1016/j.tws.2024.112865
19.
PrasadRBaxyABanerjeeA (2022) Broadband sound transmission loss in a corrugated sound panel using periodic structure theory. Journal of Vibration and Acoustics144(6): 061006. https://doi.org/10.1115/1.4055806
XiaoYCaoJWangS, et al. (2021) Sound transmission loss of plate-type metastructures: semi-Analytical modeling, elaborate analysis, and experimental validation. Mechanical Systems and Signal Processing153: 107487. https://doi.org/10.1016/j.ymssp.2020.107487
22.
ZhangXCaoZRuanL, et al. (2021) Reduction of vibration and noise in rail transit steel bridges using elastomer mats: numerical analysis and experimental validation. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit235(2): 248–261. https://doi.org/10.1177/0954409720923265
23.
ZhangXHaoCLuoH, et al. (2022) Flexural wave band gaps of steel bridge decks periodically stiffened with U-ribs: mechanism and influencing factors. Journal of Low Frequency Noise, Vibration and Active Control41(2): 799–809. https://doi.org/10.1177/14613484211068251
24.
ZhangXYouYKongD, et al. (2023) An analytical investigation into the vibration behavior of an orthotropic steel deck. Journal of Vibration and Control29(3–4): 625–635. https://doi.org/10.1177/10775463211050718
25.
ZhouHZhaoYWuH, et al. (2020) The vibroacoustic analysis of periodic structure-stiffened plates. Journal of Sound and Vibration481: 115402. https://doi.org/10.1016/j.jsv.2020.115402
