[1] [1] Yablonovitch E. Inhibited spontaneous emission in solid-state physics and electronics［J］. Physical Review Letters, 1987,58(20): 2059-2062.

[2] [2] John S. Strong localization of photons in certain disordered dielectric superlattices［J］. Physical Review Letters, 1987,58(23): 2486-2489.

[3] [3] Kushwaha M S, Halevi P, Dobrzynski L. Acoustic band structure of periodic elastic composites［J］. Physical Review Letters, 1993,71(13): 2022-2025.

[4] [4] Martínez-Sala R, Sancho J, Sánchez J V. Sound attenuation by sculpture［J］. Nature, 1995, 378(6554): 241.

[5] [5] Yang X W, Lee J S, Kim Y Y. Effective mass density based topology optimization of locally resonant acoustic metamaterials for bandgap maximization［J］. Journal of Sound and Vibration,2016,383: 89-107.

[6] [6] Tian Y P, Tan Z H, Han X, et al. Phononic crystal lens with an asymmetric scatterer［J］. Journal of Physics D: Applied Physics, 2019,52: 025102.

[7] [7] Zafar L R, Huang J, Khan M A. Quality enhancement and insertion loss reduction of a rectangular resonator by employing an ultra-wide band gap diamond phononic crystal［J］. Chinese Journal of Physics, 2020,65: 481-490.

[10] [10] Jensen J. Phononic band gaps and vibrations in one-and two-dimensional mass-spring structures［J］. Journal of Sound and Vibration,2003,266: 1053-1078.

[12] [12] Thomson W T. Transmission of elastic waves through a stratified solid medium［J］. Journal of Applied Physics,1950,21: 89-93.

[14] [14] Xu W K, Yang T Z, Wang W. Double-negative dynamic properties in one-dimensional multi-phase metamaterial based on the symmetrical equivalent layer［J］. Waves in Random and Complex Media,2013, 23(3): 258-266.

[18] [18] He J J, Kang Z. Achieving directional propagation of elastic waves via topolopgy optimization［J］. Ultrasonics,2018,82: 1-10.

[19] [19] Han X K, Zhang Z. Topological optimization of phononic crystal thin plate by a genetic algorithm［J］.Scientific Reports,2019,9: 8331.

[20] [20] Xu W K, Ning J Y, Lin Z B, et al. Multi-objective topology optimization of two-dimensional multi-phase microstructure phononic crystals［J］.Materials Today Communications,2020,22: 100801.

[21] [21] Hussein M I, Hamza K, Hulbert G M. Multiobjective evolutionary optimization of periodic layered materials for desired wave dispersion characteristics［J］.Structural Multidisciplinary Optimization,2006,31: 60-75.

[22] [22] Hussein M I, Hulbert G M, Scott R A. Dispersive elastodynamics of 1D banded materials and structures: analysis［J］.Journal of Sound and Vibration,2005,289: 779-806.

[23] [23] Hussein M I, Hulbert G M, Scott R A. Dispersive elastodynamics of 1D banded materials and structures: design［J］.Journal of Sound and Vibration,2007,307: 865-893.

[24] [24] Huang Y, Liu S T, Zhao J. A gradient-based optimization method for the design of layered phononic band-gap materials［J］. Acta Mechanica Solida Sinica,2016,29: 429-443.

[25] [25] Mathews J, Walkerm R. Mathematical methods of physics［M］. 2nd ed. USA: Benjamin-Cummings, 1970.

[26] [26] Dong H W, Su X X, Wang Y S, et al. Topological optimization of two-dimensional phononic crystals based on the finite element method and genetic algorithm［J］.Structural Multidisciplinary Optimization,2014,50: 593-604.

[27] [27] Yi G, Youn B D. A comprehensive survey on topology optimization of phononic crystals［J］.Structural Multidisciplinary Optimization,2016,54: 1315-1344.