Topological design and magnetic tunability of a novel cross‐like holes phononic crystal with low frequency

References

• M.S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafarirouhani, ACOUSTIC band structure of periodic elastic composites, Phys. Rev. Lett., vol. 71, no. 13, pp. 2022–2025, 1993. DOI: 10.1103/PhysRevLett.71.2022.
   PubMed Web of Science ®Google Scholar
• M. Kafesaki, M.M. Sigalas, and N. Garcia, Frequency modulation in the transmittivity of wave guides in elastic-wave band-gap materials, Phys. Rev. Lett., vol. 85, no. 19, pp. 4044–4047, 2000. DOI: 10.1103/PhysRevLett.85.4044.
   PubMed Web of Science ®Google Scholar
• T.T. Wu, L.C. Wu, and Z.G. Huang, Frequency band-gap measurement of two-dimensional air/silicon phononic crystals using layered slanted finger interdigital transducers, J. Appl. Phys., vol. 97, no. 9, pp. 094916, 2005. DOI: 10.1063/1.1893209.
   Web of Science ®Google Scholar
• S.I. Fomenko, M.V. Golub, C. Zhang, T.Q. Bui, and Y.S. Wang, In-plane elastic wave propagation and band-gaps in layered functionally graded phononic crystals, Int. J. Solids Struct., vol. 51, no. 13, pp. 2491–2503, 2014. DOI: 10.1016/j.ijsolstr.2014.03.017.
   Web of Science ®Google Scholar
• Z.Y. Liu et al., Locally resonant sonic materials, Science, vol. 289, no. 5485, pp. 1734–1736, 2000. DOI: 10.1126/science.289.5485.1734.
   PubMed Web of Science ®Google Scholar
• A.H. Aly, S.M. Shaban, and A. Mehaney, High-performance phoxonic cavity designs for enhanced acousto-optical interaction, Appl. Opt., vol. 60, no. 11, pp. 3224–3231, 2021. DOI: 10.1364/ao.420294.
   PubMed 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. 123503, 2012. DOI: 10.1063/1.4768934.
   Web of Science ®Google Scholar
• Y. Pennec, J.O. Vasseur, B. Djafari-Rouhani, L. Dobrzynski, and P.A. Deymier, Two-dimensional phononic crystals: Examples and applications, Surf. Sci. Rep., vol. 65, no. 8, pp. 229–291, 2010. DOI: 10.1016/j.surfrep.2010.08.002.
   Web of Science ®Google Scholar
• A.H. Aly, A. Nagaty, Z. Khalifa, and A. Mehaney, The significance of temperature dependence on the piezoelectric energy harvesting by using a phononic crystal, J. Appl. Phys., vol. 123, no. 18, pp. 185102, 2018. DOI: 10.1063/1.5019623.
   Web of Science ®Google Scholar
• H.Y. Bao, Y.Z. Wang, and Y.S. Wang, Elastic wave cloak and invisibility of piezoelectric/piezomagnetic mechanical metamaterials, J. Acoust. Soc. Am., vol. 148, no. 6, pp. 3722–3736, 2020. DOI: 10.1121/10.0002777.
   PubMed Web of Science ®Google Scholar
• S.M. Shaban, A. Mehaney, and A.H. Aly, Determination of 1-propanol, ethanol, and methanol concentrations in water based on a one-dimensional phoxonic crystal sensor, Appl. Opt., vol. 59, no. 13, pp. 3878–3885, 2020. DOI: 10.1364/ao.388763.
   PubMed Web of Science ®Google Scholar
• S.E. Zaki, A. Mehaney, H.M. Hassanein, and A.H. Aly, High-performance liquid sensor based one-dimensional phononic crystal with demultiplexing capability, Mater. Today Commun., vol. 26, pp. 102045, 2021. DOI: 10.1016/j.mtcomm.2021.102045.
   Web of Science ®Google Scholar
• Y.F. Wang, Y.Z. Wang, B. Wu, C. Wq, and Y.S. Wang, Tunable and active phononic crystals and metamaterials, Appl. Mech. Rev., vol. 72, no. 4, pp. 040801, 2020. DOI: 10.1115/1.4046222.
   Web of Science ®Google Scholar
• Y.L. Huang, J. Li, W.Q. Chen, and R.H. Bao, Tunable bandgaps in soft phononic plates with spring-mass-like resonators, Int. J. Mech. Sci., vol. 151, pp. 300–313, 2019. DOI: 10.1016/j.ijmecsci.2018.11.029.
   Web of Science ®Google Scholar
• X.W. Xue, P. Li, and F. Jin, The tunable one-way transmission of Lamb waves by using giant magnetostrictive materials, Appl. Phys. Express, vol. 14, no. 4, pp. 044002, 2021. DOI: 10.35848/1882-0786/abdcd7.
   PubMed Web of Science ®Google Scholar
• L. Ning, Y.Z. Wang, and Y.S. Wang, Active control cloak of the elastic wave metamaterial, Int. J. Solids Struct., vol. 202, pp. 126–135, 2020. DOI: 10.1016/j.ijsolstr.2020.06.009.
   Web of Science ®Google Scholar
• O.B. Matar et al., Band gap tunability of magneto-elastic phononic crystal, J. Appl. Phys., vol. 111, no. 5, pp. 054901, 2012. DOI: 10.1063/1.3687928.
   Web of Science ®Google Scholar
• Z.L. Xu, F.G. Wu, and Z.N. Guo, Shear-wave band gaps tuned in two-dimensional phononic crystals with magnetorheological material, Solid State Commun., vol. 154, pp. 43–45, 2013. DOI: 10.1016/j.ssc.2012.10.040.
   Web of Science ®Google Scholar
• F. Motaei, A. Bahrami, and H.B. Ghavifekr, Magnetically controlled three-channel phononic switch, Mech. Adv. Mater. Struct. Advance online publication. 2021. DOI: 10.1080/15376494.2021.1931733.
   Web of Science ®Google Scholar
• A.M. Ahmed, A. Mehaney, M. Shaban, and A.H. Aly, Scattering spectra of magneto-plasmonic core/shell nanoparticle based on Mie theory, Mater. Res. Express, vol. 6, no. 8, pp. 085073, 2019. DOI: 10.1088/2053-1591/ab2145.
   Web of Science ®Google Scholar
• S.E. Zaki, A. Mehaney, H.M. Hassanein, and A.H. Aly, Fano resonance based defected 1D phononic crystal for highly sensitive gas sensing applications, Sci. Rep., vol. 10, no. 1, pp. 17979, 2020. DOI: 10.1038/s41598-020-75076-8.
   PubMed Web of Science ®Google Scholar
• A.H. Aly, A. Nagaty, and A. Mehaney, One-dimensional phononic crystals that incorporate a defective piezoelectric/piezomagnetic as a new sensor, Eur. Phys. J. B, vol. 91, no. 10, pp. 211, 2018. DOI: 10.1140/epjb/e2018-90347-6.
   Web of Science ®Google Scholar
• A. Aly, A. Nagaty, and A. Mehaney, Thermal properties of one-dimensional piezoelectric phononic crystal, Eur. Phys. J. B, vol. 91, no. 10, pp. 251, 2018. DOI: 10.1140/epjb/e2018-90297-y.
   Web of Science ®Google Scholar
• A.O. Krushynska, A. Amendola, F. Bosia, C. Daraio, N.M. Pugno, and F. Fraternali, Accordion-like metamaterials with tunable ultra-wide low-frequency band gaps, New J. Phys., pp. 20, pp. 073051, 2018. DOI: 10.1088/1367-2630/aad354.
   Web of Science ®Google Scholar
• Y.F. Li, F. Meng, S. Li, B.H. Jia, S.W. Zhou, and X.D. Huang, Designing broad phononic band gaps for in-plane modes, Phys. Lett. A, vol. 382, no. 10, pp. 679–684, 2018. DOI: 10.1016/j.physleta.2017.12.050.
   Web of Science ®Google Scholar
• X.W. Sun, H.F. Zhu, X.L. Gao, T. Song, and Z.J. Liu, Tunable low-frequency bandgaps of a new two-dimensional multi-component phononic crystal under different pressures, geometric parameters and pre-compression strains, Mech. Adv. Mater. Struct. Advance online publication. 2021. DOI: 10.1080/15376494.2021.1916139.
   Web of Science ®Google Scholar
• A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, Complete band gaps in two-dimensional phononic crystal slabs, Phys. Rev. E., vol. 74, no. 4 Pt 2, pp. 046610, 2006. DOI:10.1103/PhysRevE.74.046610.
   PubMed Web of Science ®Google Scholar
• S. Mohammadi et al., Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates, Electron. Lett., vol. 43, no. 16, pp. 898–899, 2007. DOI: 10.1049/el:20071159.
   Web of Science ®Google Scholar
• Y.F. Wang, Y.S. Wang, and X.X. Su, Large bandgaps of two-dimensional phononic crystals with cross-like holes, J. Appl. Phys., vol. 110, no. 11, pp. 113520, 2011. DOI: 10.1063/1.3665205.
   Web of Science ®Google Scholar
• S. Jiang, H. Chen, L.X. Dai, H.P. Hua, and V. Laude, Multiple low-frequency broad band gaps generated by a phononic crystal of periodic circular cavity sandwich plates, Compos. Struct., vol. 176, pp. 294–303, 2017. DOI: 10.1016/j.compstruct.2017.05.048.
   Web of Science ®Google Scholar
• X. Li, S.W. Ning, Z.L. Liu, Z.M. Yan, C.C. Luo, and Z. Zhuang, Designing phononic crystal with anticipated band gap through a deep learning based data-driven method, Comput. Meth. Appl. Mech. Eng., vol. 361, pp. 112737, 2020. DOI: 10.1016/j.cma.2019.112737.
   Web of Science ®Google Scholar
• C. C. Luo, S. W. Ning, Z. L. Liu, and Z. Zhuang, Interactive inverse design of layered phononic crystals based on reinforcement learning, Extreme Mech Lett., vol. 36, pp. 100651, 2020. DOI: 10.1016/j.eml.2020.100651.
   Web of Science ®Google Scholar
• S.H. Xiao, C. Zhang, Q.H. Qin, and H. Wang, A novel planar auxetic phononic crystal with periodic cookie-shaped cellular microstructures, Mech. Adv. Mater. Struct. Advance online publication. 2021. DOI: 10.1080/15376494.2021.1896057.
   Web of Science ®Google Scholar
• O.R. Bilal and M.I. Hussein, Ultrawide phononic band gap for combined in-plane and out-of-plane waves, Phys. Rev. E., vol. 84, no. 6 Pt 2, pp. 065701, 2011. DOI: 10.1103/PhysRevE.84.065701.
   Web of Science ®Google Scholar
• S. Hedayatrasa, K. Abhary, M. Uddin, and C.T. Ng, Optimum design of phononic crystal perforated plate structures for widest bandgap of fundamental guided wave modes and maximized in-plane stiffness, J. Mech. Phys. Solids, vol. 89, pp. 31–58, 2016. DOI: 10.1016/j.jmps.2016.01.010.
   Web of Science ®Google Scholar
• Y.B. Song, L.P. Feng, J.H. Wen, D.L. Yu, and X.S. Wen, Reduction of the sound transmission of a periodic sandwich plate using the stop band concept, Compos. Struct., vol. 128, pp. 428–436, 2015. DOI: 10.1016/j.compstruct.2015.02.053.
   Web of Science ®Google Scholar
• P. Wang, F. Casadei, S.C. Shan, J.C. Weaver, and K. Bertoldi, Harnessing buckling to design tunable locally resonant acoustic metamaterials, Phys. Rev. Lett., vol. 113, no. 1, pp. 014301, 2014. DOI: 10.1103/PhysRevLett.113.014301.
   PubMed Web of Science ®Google Scholar
• E. Coffy, T. Lavergne, M. Addouche, S. Euphrasie, P. Vairac, and A. Khelif, Ultra-wide acoustic band gaps in pillar-based phononic crystal strips, J. Appl. Phys., vol. 118, no. 21, pp. 214902, 2015. DOI: 10.1063/1.4936836.
   Web of Science ®Google Scholar
• Z.Y. Lian, H.P. Hu, L.X. Dai, Y.X. Liang, B. Luo, and X.D. Chen, Coupling between two kinds of band gaps of a shunted tube piezoelectric phononic crystal, J. Intell. Mater. Syst. Struct., vol. 28, no. 16, pp. 2153–2166, 2017. DOI: 10.1177/1045389X16685437.
   Web of Science ®Google Scholar
• A. Gersborg-Hansen, O. Sigmund, and R.B. Haber, Topology optimization of channel flow problems, Struct. Multidisc. Optim., vol. 30, no. 3, pp. 181–192, 2005. DOI: 10.1007/s00158-004-0508-7.
   Web of Science ®Google Scholar
• X.P. Zhang, J. Xing, P. Liu, Y.J. Luo, and Z. Kang, Realization of full and directional band gap design by non-gradient topology optimization in acoustic metamaterials, Extreme Mech. Lett., vol. 42, pp. 101126, 2021. DOI: 10.1016/j.eml.2020.101126.
   Web of Science ®Google Scholar
• H.W. Dong, S.D. Zhao, Y.S. Wang, and C.Z. Zhang, Topology optimization of anisotropic broadband double-negative elastic metamaterials, J. Mech. Phys. Solids, vol. 105, pp. 54–80, 2017. DOI: 10.1016/j.jmps.2017.04.009.
   Web of Science ®Google Scholar
• Q. Cheng, H. Guo, T. Yuan, P. Sun, F.X. Guo, and Y.S. Wang, Topological design of square lattice structure for broad and multiple band gaps in low-frequency range, Extreme Mech. Lett., vol. 35, pp. 100632, 2020. DOI: 10.1016/j.eml.2020.100632.
   Web of Science ®Google Scholar
• T.E. Bruns and D.A. Tortorelli, Topology optimization of non-linear elastic structures and compliant mechanisms, Comput. Meth. Appl. Mech. Eng., vol. 190, no. 26–27, pp. 3443–3459, 2001. DOI: 10.1016/S0045-7825(00)00278-4.
   Web of Science ®Google Scholar
• O. Sigmund and S. Torquato, Design of materials with extreme thermal expansion using a three-phase topology optimization method, J. Mech. Phys. Solids, vol. 45, no. 6, pp. 1037–1067, 1997. DOI: 10.1016/S0022-5096(96)00114-7.
   Web of Science ®Google Scholar
• A.H. Safavi-Naeini, J.T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, Two-dimensional phononic-photonic band gap optomechanical crystal cavity, Phys. Rev. Lett., vol. 112, no. 15, pp. 153603, 2014. DOI: 10.1103/PhysRevLett.112.153603.
   PubMed Web of Science ®Google Scholar
• S. Jiang, H.P. Hu, and V. Laude, Ultra-wide band gap in two-dimensional phononic crystal with combined convex and concave holes, Phys. Status Solidi rrl, vol. 12, no. 2, pp. 1700317, 2018. DOI: 10.1002/pssr.20.
   Google Scholar
• S. Jiang, H.P. Hu and V. Laude, Low-frequency band gap in cross-like holey phononic crystal strip, J. Phys. D-Appl. Phys., vol. 51, no. 4, pp. 045601, 2018. DOI: 10.1088/1361-6463/aa9ec1.
   Web of Science ®Google Scholar
• L.D. Landau and E.M. Lifshitz, Theory of Elasticity, Pergamon Press, New York, 1959.
   Google Scholar
• M.R. Jolly, J.D. Carlson, B.C. Munoz, and T.A. Bullions, The magnetoviscoelastic response of elastomer composites consisting of ferrous particles embedded in a polymer matrix, J. Intell. Mater. Syst. Struct., vol. 7, no. 6, pp. 613–622, 1996. DOI: 10.1177/1045389X9600700601.
   Web of Science ®Google Scholar
• L. Davis, Model of magnetorheological elastomers, J. Appl. Phys., vol. 85, no. 6, pp. 3348–3351, 1999. DOI: 10.1063/1.369682.
   Web of Science ®Google Scholar