Band gap characteristics of two-dimensional functionally graded periodic grid structures with local resonators

References

• L. Brillouin, Wave Propagation in Periodic Structures, Dover Publication Incorporated, New York, 1946.
   Google Scholar
• R. Martínez-Sala, J. Sancho, J. V. Sánchez, V. Gómez, J. Llinares, and F. Meseguer, Sound attenuation by sculpture, Nature., vol. 378, no. 6554, pp. 241–241, 1995. DOI: 10.1038/378241a0.
   Web of Science ®Google Scholar
• F. Yu, et al., Structural design and band gap properties of 3D star-shaped single-phase metamaterials, J. Vib. Eng. Technol., vol. 10, pp. 9, 2022.
   Web of Science ®Google Scholar
• C. Wang, X. Yao, G. Wu, and L. Tang, Complete vibration band gap characteristics of two-dimensional periodic grid structures, Compos. Struct., vol. 274, pp. 1–9, 2021.
   Web of Science ®Google Scholar
• H. Jafari, S. Sepehri, M. R. H. Yazdi, M. M. Mashhadi, and M. M. S. Fakhrabadi, Hybrid lattice metamaterials with auxiliary resonators made of functionally graded materials, Acta Mech., vol. 231, no. 12, pp. 4835–4849, 2020. DOI: 10.1007/s00707-020-02799-0.
   Web of Science ®Google Scholar
• A. Srikantha Phani, J. Woodhouse, and N. A. Fleck, Wave propagation in two-dimensional periodic lattices, J. Acoust. Soc. Am., vol. 119, no. 4, pp. 1995–2005, 2006. DOI: 10.1121/1.2179748.
   PubMed Web of Science ®Google Scholar
• G. Trainiti, J. J. Rimoli, and M. Ruzzene, Wave propagation in undulated structural lattices, Int. J. Solids Struct., vol. 97-98, pp. 431–444, 2016. DOI: 10.1016/j.ijsolstr.2016.07.006.
   Web of Science ®Google Scholar
• Y. L. Li, and H. Q. Zhang, Band gap mechanism and vibration attenuation characteristics of the quasi-one-dimensional tetra-chiral metamaterial, Eur. J. Mech. A-Solids., vol. 92, pp. 17, 2022.
   Web of Science ®Google Scholar
• L. Tang, X. Yao, G. Wu, and D. Tang, Band gaps characteristics analysis of periodic oscillator coupled damping beam, Materials., vol. 13, no. 24, pp. 5748, 2020. DOI: 10.3390/ma13245748.
   PubMed Web of Science ®Google Scholar
• I. L. Chang, Z.-X. Liang, H.-W. Kao, S.-H. Chang, and C.-Y. Yang, The wave attenuation mechanism of the periodic local resonant metamaterial, J. Sound Vib., vol. 412, pp. 349–359, 2018. DOI: 10.1016/j.jsv.2017.10.008.
   Web of Science ®Google Scholar
• M. Mazzotti, I. Bartoli, and M. Miniaci, Modeling bloch waves in prestressed phononic crystal plates, Front. Mater., vol. 6, pp. 1–9, 2019. DOI: 10.3389/fmats.2019.00074.
   Web of Science ®Google Scholar
• L. J. Lei, L. C. Miao, C. Li, X. D. Liang, and J. J. Wang, The effects of composite primitive cells on band gap property of locally resonant phononic crystal, Mod. Phys. Lett. B., vol. 35, no. 20, pp. 2150334, 2021. DOI: 10.1142/S0217984921503346.
   Web of Science ®Google Scholar
• A. Stein, M. Nouh, and T. Singh, Widening, transition and coalescence of local resonance band gaps in multi-resonator acoustic metamaterials: From unit cells to finite chains, J. Sound Vib., vol. 523, pp. 20, 2022.
   Web of Science ®Google Scholar
• Z. Y. Liu, et al., Locally resonant sonic materials, Science (New York, N.Y.)., vol. 289, no. 5485, pp. 1734–1736, 2000. DOI: 10.1126/science.289.5485.1734.
   PubMed Web of Science ®Google Scholar
• D. M. Mead, Wave propagation in continuous periodic structures: research contributions from southampton, 1964–1995, J. Sound Vib., vol. 190, no. 3, pp. 495–524, 1996. DOI: 10.1006/jsvi.1996.0076.
   Web of Science ®Google Scholar
• M.-L. Wu, L.-Y. Wu, W.-P. Yang, and L.-W. Chen, Elastic wave band gaps of one-dimensional phononic crystals with functionally graded materials, Smart Mater. Struct., vol. 18, no. 11, pp. 115013, 2009. DOI: 10.1088/0964-1726/18/11/115013.
   Web of Science ®Google Scholar
• G. Carta, G. F. Giaccu, and M. Brun, A phononic band gap model for long bridges. The ‘Brabau’ bridge case, Eng. Struct., vol. 140, pp. 66–76, 2017. DOI: 10.1016/j.engstruct.2017.01.064.
   Web of Science ®Google Scholar
• D. Richards, and D. J. Pines, Passive reduction of gear mesh vibration using a periodic drive shaft, J. Sound Vib., vol. 264, no. 2, pp. 317–342, 2003. DOI: 10.1016/S0022-460X(02)01213-0.
   Web of Science ®Google Scholar
• C. Li, S. Zhang, L. Gao, W. Huang, Z. Liu, and J. Wang, Vibration attenuation investigations on a distributed phononic crystals beam for rubber concrete structures, Math. Prob. Eng., vol. 2021, pp. 1–14, 2021.
   Web of Science ®Google Scholar
• F. Gao, Z. Wu, F. Li, and C. Zhang, Numerical and experimental analysis of the vibration and band-gap properties of elastic beams with periodically variable cross sections, Waves Random Complex Media., vol. 29, no. 2, pp. 299–316, 2019. DOI: 10.1080/17455030.2018.1430918.
   Web of Science ®Google Scholar
• Z. K. Guo, G. B. Hu, V. Sorokin, L. H. Tang, X. D. Yang, and J. Zhang, Low-frequency flexural wave attenuation in metamaterial sandwich beam with hourglass lattice truss core, Wave Motion., vol. 104, pp. 102750, 2021. DOI: 10.1016/j.wavemoti.2021.102750.
   Web of Science ®Google Scholar
• D. Tang, L. Li, Z. Zhang, and S. Wu, Propagation and attenuation characteristics of free flexural waves in multi-stepped periodic beams by the method of reverberation-ray matrix, Waves Random Complex Media., pp. 1–27, 2021. DOI: 10.1080/17455030.2021.1931553.
   Web of Science ®Google Scholar
• L. X. Xie, B. Z. Xia, J. Liu, G. L. Huang, and J. R. Lei, An improved fast plane wave expansion method for topology optimization of phononic crystals, Int. J. Mech. Sci., vol. 120, pp. 171–181, 2017. DOI: 10.1016/j.ijmecsci.2016.11.023.
   Web of Science ®Google Scholar
• Y. Zhang, Z. Q. Ni, L. Han, Z. M. Zhang, and H. Y. Chen, Study of improved plane wave expansion method on phononic crystal, Optoelectron. Adv. Mater.-Rapid Commun., vol. 5, no. 8, pp. 870–873, 2011.
   Web of Science ®Google Scholar
• J. Z. Sun, and P. J. Wei, Band gaps of 2D phononic crystal with imperfect interface, Mech. Adv. Mater. Struct., vol. 21, no. 2, pp. 107–116, 2014. DOI: 10.1080/15376494.2012.677110.
   Web of Science ®Google Scholar
• M. Hajhosseini, and A. M. Parrany, Study on in-plane band gap characteristics of a circular periodic structure using DQM, Int. J. Appl. Mechanics., vol. 12, no. 07, pp. 2050083, 2020. DOI: 10.1142/S1758825120500830.
   Google Scholar
• C. L. Wang, X. L. Yao, G. X. Wu, and L. Tang, Vibration band gap characteristics of two-dimensional periodic double-wall grillages, Materials., vol. 14, no. 23, pp. 7174, 2021. DOI: 10.3390/ma14237174.
   PubMed Web of Science ®Google Scholar
• Y. Li, Q. Zhou, L. Zhou, L. Zhu, and K. Guo, Flexural wave band gaps and vibration attenuation characteristics in periodic bi-directionally orthogonal stiffened plates, Ocean Eng., vol. 178, pp. 95–103, 2019. DOI: 10.1016/j.oceaneng.2019.02.076.
   Web of Science ®Google Scholar
• X. N. Liu, G. K. Hu, C. T. Sun, and G. L. Huang, Wave propagation characterization and design of two-dimensional elastic chiral metacomposite, J. Sound Vib., vol. 330, no. 11, pp. 2536–2553, 2011. DOI: 10.1016/j.jsv.2010.12.014.
   Web of Science ®Google Scholar
• Y. K. Dong, H. Yao, J. Du, J. B. Zhao, and C. Ding, Research on bandgap property of a novel small size multi-band phononic crystal, Phys. Lett. A., vol. 383, no. 4, pp. 283–288, 2019. DOI: 10.1016/j.physleta.2018.10.042.
   Web of Science ®Google Scholar
• J. Hong, X. He, D. Zhang, B. Zhang, and Y. Ma, Vibration isolation design for periodically stiffened shells by the wave finite element method, J. Sound Vib., vol. 419, pp. 90–102, 2018. DOI: 10.1016/j.jsv.2017.12.035.
   Web of Science ®Google Scholar
• S. Wen, Y. Xiong, S. Hao, F. Li, and C. Zhang, Enhanced band-gap properties of an acoustic metamaterial beam with periodically variable cross-sections, Int. J. Mech. Sci., vol. 166, pp. 1–10, 2020.
   Web of Science ®Google Scholar
• S. L. Zuo, F. M. Li, and C. Z. Zhang, Numerical and experimental investigations on the vibration band-gap properties of periodic rigid frame structures, Acta Mech., vol. 227, no. 6, pp. 1653–1669, 2016. DOI: 10.1007/s00707-016-1587-4.
   Web of Science ®Google Scholar
• T. Ren, F. M. Li, Y. N. Chen, C. C. Liu, and C. Z. Zhang, Improvement of the band-gap characteristics of active composite laminate metamaterial plates, Compos. Struct., vol. 254, pp. 13, 2020.
   Web of Science ®Google Scholar
• J. F. Doyle, and T. Farris, A spectrally formulated finite element for flexural wave propagation in beams, Int. J. Anal. Exp. Modal Anal., vol. 5, pp. 13–23, 1990.
   Google Scholar
• J. F. Doyle, A spectrally formulated finite element for longitudinal wave propagation, Int. J. Anal. Exp. Modal Anal., vol. 3, pp. 1–5, 1988.
   Google Scholar
• J. F. Doyle, Wave Propagation in Structures: spectral Analysis Using Fast Discrete Fourier Transforms, Springer-Verlag New York, 1997.
   Google Scholar
• Z. J. Wu, and F. M. Li, Spectral element method and its application in analysing the vibration band gap properties of two-dimensional square lattices, J. Vib. Control., vol. 22, no. 3, pp. 710–721, 2016. DOI: 10.1177/1077546314531805.
   Web of Science ®Google Scholar
• Z. J. Wu, F. M. Li, and C. Z. Zhang, Vibration band-gap properties of three-dimensional Kagome lattices using the spectral element method, J. Sound Vib., vol. 341, pp. 162–173, 2015. DOI: 10.1016/j.jsv.2014.12.038.
   Web of Science ®Google Scholar
• D. S. Wang, P. Zhou, T. Jin, and H. P. Zhu, Damage identification for beam structures using the laplace transform-based spectral element method and strain statistical moment, J. Aerosp. Eng., vol. 31, no. 3, pp. 04018016, 2018. DOI: 10.1061/(ASCE)AS.1943-5525.0000838.
   Web of Science ®Google Scholar
• R. L. Lucena, and J. M. C. Dos Santos, Structural health monitoring using time reversal and cracked rod spectral element, Mech. Syst. Sig. Process., vol. 79, pp. 86–98, 2016. DOI: 10.1016/j.ymssp.2016.02.044.
   Web of Science ®Google Scholar
• P. Ghaderi, S. I. Rich, and A. J. Dick, Asme and, "Spectral-domain based impact force identification for rod structures", in: ASME International Mechanical Engineering Congress and Exposition (IMECE2013), Amer Soc Mechanical Engineers, San Diego, CA, 2013. DOI: 10.1115/IMECE2013-64892.
   Google Scholar
• P. Ghaderi, A. J. Dick, J. R. Foley, and G. Falbo, Practical high-fidelity frequency-domain force and location identification, Comput. Struct., vol. 158, pp. 30–41, 2015. DOI: 10.1016/j.compstruc.2015.05.028.
   Web of Science ®Google Scholar
• M. Espo, M. H. Abolbashari, and S. M. Hosseini, Band structure analysis of wave propagation in piezoelectric nano-metamaterials as periodic nano-beams considering the small scale and surface effects, Acta Mech., vol. 231, no. 7, pp. 2877–2893, 2020. DOI: 10.1007/s00707-020-02678-8.
   Web of Science ®Google Scholar
• D. Qian, Wave propagation in a thermo-magneto-mechanical phononic crystal nanobeam with surface effects, J Mater Sci., vol. 54, no. 6, pp. 4766–4779, 2019. DOI: 10.1007/s10853-018-03208-7.
   Web of Science ®Google Scholar
• A. G. De Miguel, M. Cinefra, M. Filippi, A. Pagani, and E. Carrera, Validation of FEM models based on Carrera Unified Formulation for the parametric characterization of composite metamaterials, J. Sound Vib., vol. 498, pp. 1–17, 2021.
   Web of Science ®Google Scholar
• S. I. Fomenko, M. V. Golub, A. Chen, Y. Wang, and C. Zhang, Band-gap and pass-band classification for oblique waves propagating in a three-dimensional layered functionally graded piezoelectric phononic crystal, J. Sound Vib., vol. 439, pp. 219–240, 2019. DOI: 10.1016/j.jsv.2018.09.059.
   Web of Science ®Google Scholar
• H. N. Nguyen, T. T. Hong, P. V. Vinh, and D. V. Thom, An efficient beam element based on quasi-3D theory for static bending analysis of functionally graded beams, Materials., vol. 12, no. 13, pp. 2198, 2019. DOI: 10.3390/ma12132198.
   PubMed Web of Science ®Google Scholar
• Y. Chen, et al., Free transverse vibrational analysis of axially functionally graded tapered beams via the variational iteration approach, J. Vib. Control., vol. 27, no. 11-12, pp. 1265–1280, 2021. DOI: 10.1177/1077546320940181.
   Web of Science ®Google Scholar
• U. Gul, M. Aydogdu, and F. Karacam, Dynamics of a functionally graded Timoshenko beam considering new spectrums, Compos. Struct., vol. 207, pp. 273–291, 2019. DOI: 10.1016/j.compstruct.2018.09.021.
   Web of Science ®Google Scholar
• A. Chakraborty, and S. Gopalakrishnan, A spectrally formulated finite element for wave propagation analysis in functionally graded beams, Int. J. Solids Struct., vol. 40, no. 10, pp. 2421–2448, 2003. DOI: 10.1016/S0020-7683(03)00029-5.
   Web of Science ®Google Scholar
• M. M. Gasik, Functionally graded materials bulk processing techniques, IJMPT., vol. 39, no. 1/2, pp. 20–29, 2010. DOI: 10.1504/IJMPT.2010.034257.
   Web of Science ®Google Scholar
• M. Naebe, and K. Shirvanimoghaddam, Functionally graded materials: A review of fabrication and properties, Appl. Mater. Today., vol. 5, pp. 223–245, 2016. DOI: 10.1016/j.apmt.2016.10.001.
   Web of Science ®Google Scholar
• X.-L. Su, Y.-W. Gao, and Y.-H. Zhou, The influence of material properties on the elastic band structures of one-dimensional functionally graded phononic crystals, J. Appl. Phys., vol. 112, no. 12, pp. 1–8, 2012.
   Web of Science ®Google Scholar
• L. M. Gao, Z. Zhong, and C. Z. Zhang, Flexural wave in an functionally graded periodic beam, Adv. Vib. Eng., vol. 12, no. 2, pp. 157–163, 2013.
   Google Scholar
• J. Li, P. Yang, and S. Li, Multiple band gaps for efficient wave attenuation by inertial amplification in periodic functionally graded beams, Compos. Struct., vol. 271, pp. 1–16, 2021.
   Web of Science ®Google Scholar
• M. V. Golub, S. I. Fomenko, T. Q. Bui, C. Zhang, and Y. S. Wang, Transmission and band gaps of elastic SH waves in functionally graded periodic laminates, Int. J. Solids Struct., vol. 49, no. 2, pp. 344–354, 2012. DOI: 10.1016/j.ijsolstr.2011.10.013.
   Web of Science ®Google Scholar
• S. Sepehri, H. Jafari, M. Mosavi Mashhadi, M. R. Hairi Yazdi, and M. M. Seyyed Fakhrabadi, Tunable elastic wave propagation in planar functionally graded metamaterials, Acta Mech., vol. 231, no. 8, pp. 3363–3385, 2020. DOI: 10.1007/s00707-020-02705-8.
   Web of Science ®Google Scholar
• L. Hadji, Z. Khelifa, and A. B. El Abbes, A new higher order shear deformation model for functionally graded beams, KSCE J Civ Eng., vol. 20, no. 5, pp. 1835–1841, 2016. DOI: 10.1007/s12205-015-0252-0.
   Web of Science ®Google Scholar