[1] R.D. Woods, Screening of surface wave in soils, Journal of the soil mechanics and foundations division, 94(4) (1968) 951-979.
[2] E. Çelebi, S. Fırat, G. Beyhan, İ. Çankaya, İ. Vural, O. Kırtel, Field experiments on wave propagation and vibration isolation by using wave barriers, Soil dynamics and earthquake engineering, 29(5) (2009) 824-833.
[3] T.W. May, B.A. Bolt, The effectiveness of trenches in reducing seismic motion, Earthquake Engineering & Structural Dynamics, 10(2) (1982) 195-210.
[4] M. Adam, O. Von Estorff, Reduction of train-induced building vibrations by using open and filled trenches, Computers & Structures, 83(1) (2005) 11-24.
[5] M.-m. Sun, C. Chen, W.-y. Chen, X. Ping, Analysis on multiple scattering by an arbitrary configuration of piles as barriers for vibration isolation, Soil Dynamics and Earthquake Engineering, 31(3) (2011) 535-545.
[6] J. Avilés, F.J. Sánchez-Sesma, Foundation isolation from vibrations using piles as barriers, Journal of Engineering Mechanics, 114(11) (1988) 1854-1870.
[7] F.E. Richart, J.R. Hall, R.D. Woods, Vibrations of soils and foundations, (1970).
[8] Y.-Q. Cai, G.-Y. Ding, C.-J. Xu, Amplitude reduction of elastic waves by a row of piles in poroelastic soil, Computers and Geotechnics, 36(3) (2009) 463-473.
[9] F. Yarmohammadi, R. Rafiee-Dehkharghani, An optimal design procedure of wave barriers for mitigation of underground and above-ground railway vibrations, International Journal of Structural Stability and Dynamics, 20(11) (2020) 2050121.
[10] K.M. Dolatshahi, A. Rezaie, R. Rafiee-Dehkharghani, Topology optimization of wave barriers for mitigation of vertical component of seismic ground motions, Journal of Earthquake Engineering, 24(1) (2020) 84-108.
[11] F. Yarmohammadi, R. Rafiee-Dehkharghani, C. Behnia, A. Aref, Design of wave barriers for mitigation of train–induced vibrations using a coupled genetic-algorithm/finite-element methodology, Soil Dynamics and Earthquake Engineering, 121 (2019) 262-275.
[12] F. Yarmohammadi, R. Rafiee-Dehkharghani, C. Behnia, A. Aref, Topology optimization of jet-grouted overlapping columns for mitigation of train-induced ground vibrations, Construction and Building Materials, 190 (2018) 838-850.
[13] A. Rezaie, R. Rafiee-Dehkharghani, K.M. Dolatshahi, S.R. Mirghaderi, Soil-buried wave barriers for vibration control of structures subjected to vertically incident shear waves, Soil Dynamics and Earthquake Engineering, 109 (2018) 312-323.
[14] S. Kattis, D. Polyzos, D. Beskos, Modelling of pile wave barriers by effective trenches and their screening effectiveness, Soil Dynamics and Earthquake Engineering, 18(1) (1999) 1-10.
[15] S. Ahmad, T. Al-Hussaini, Simplified design for vibration screening by open and in-filled trenches, Journal of geotechnical engineering, 117(1) (1991) 67-88.
[16] S. Amanat, K. Gholami, R. Rafiee-Dehkharghani, D. Bansal, Plane waves mitigation in saturated porous media using optimal periodic wave barriers, Applied Acoustics, 200 (2022) 109085.
[17] J. Huang, Z. Shi, Application of periodic theory to rows of piles for horizontal vibration attenuation, International Journal of Geomechanics, 13(2) (2013) 132-142.
[18] X. Pu, Z. Shi, Periodic pile barriers for Rayleigh wave isolation in a poroelastic half-space, Soil Dynamics and Earthquake Engineering, 121 (2019) 75-86.
[19] Q. Meng, Z. Shi, Propagation attenuation of plane waves in single-phased soil by periodic pile barriers, International Journal of Geomechanics, 18(6) (2018) 04018035.
[20] Z. Shi, Y. Wen, Q. Meng, Propagation attenuation of plane waves in saturated soil by pile barriers, International Journal of Geomechanics, 17(9) (2017) 04017053.
[21] X. Liu, Z. Shi, Y. Mo, Comparison of 2D and 3D models for numerical simulation of vibration reduction by periodic pile barriers, Soil Dynamics and Earthquake Engineering, 79 (2015) 104-107.
[22] J. Huang, Z. Shi, Vibration reduction of plane waves using periodic in-filled pile barriers, Journal of Geotechnical and Geoenvironmental Engineering, 141(6) (2015) 04015018.
[23] J. Huang, Z. Shi, Attenuation zones of periodic pile barriers and its application in vibration reduction for plane waves, Journal of Sound and Vibration, 332(19) (2013) 4423-4439.
[24] G. Jia, Z. Shi, A new seismic isolation system and its feasibility study, Earthquake Engineering and Engineering Vibration, 9(1) (2010) 75-82.
[25] S. Amanat, R. Rafiee-Dehkharghani, Investigation of periodic resonators as wave barriers for mitigating surface seismic waves using Bloch-Floquet theory, Sharif Journal of Civil Engineering, (2023).
[26] S. Amanat, R. Rafiee-Dehkharghani, M. Bitaraf, D. Bansal, Analytical and numerical investigation of finite and infinite periodic lattices for mitigation of seismic waves in layered grounds, International Journal of Engineering Science, 173 (2022) 103655.
[27] Muhammad, T. Wu, C. Lim, Forest trees as naturally available seismic metamaterials: low frequency Rayleigh wave with extremely wide bandgaps, International Journal of Structural Stability and Dynamics, 20(14) (2020) 2043014.
[28] C. Lim, J. Reddy, Built-up structural steel sections as seismic metamaterials for surface wave attenuation with low frequency wide bandgap in layered soil medium, Engineering Structures, 188 (2019) 440-451.
[29] C. Lim, K.K. Żur, Wide Rayleigh waves bandgap engineered metabarriers for ground born vibration attenuation, Engineering Structures, 246 (2021) 113019.
[30] M.M. Hajjaj, J. Tu, Wave attenuation study on a wide-band seismic metasurface using capped pillars, Comptes Rendus. Mécanique, 350(G2) (2022) 237-254.
[31] K. Gholami, R. Rafiee-Dehkharghani, A. Ghalandarzadeh, Shear and compression waves screening in 2D for dry or saturated ground using periodic infinite and finite soil-foam barriers, Archive of Applied Mechanics, (2022) 1-21.
[32] X. Pu, Z. Shi, A novel method for identifying surface waves in periodic structures, Soil Dynamics and Earthquake Engineering, 98 (2017) 67-71.
[33] Y.-f. Liu, J.-k. Huang, Y.-g. Li, Z.-f. Shi, Trees as large-scale natural metamaterials for low-frequency vibration reduction, Construction and Building Materials, 199 (2019) 737-745.
[34] X. Pu, Z. Shi, H. Xiang, Feasibility of ambient vibration screening by periodic geofoam-filled trenches, Soil Dynamics and Earthquake Engineering, 104 (2018) 228-235.
[35] C. Comi, L. Driemeier, Wave propagation in cellular locally resonant metamaterials, Latin American Journal of Solids and Structures, 15 (2018).
[36] L. Brillouin, Wave propagation in periodic structures: electric filters and crystal lattices, (1946).
[37] C. Kittel, P. McEuen, P. McEuen, Introduction to solid state physics, Wiley New York, 1996.
[38] Z. Cheng, Z. Shi, Composite periodic foundation and its application for seismic isolation, Earthquake Engineering & Structural Dynamics, 47(4) (2018) 925-944.
[39] COMSOL, Multiphysics® v. 5.6.
www.comsol.com. COMSOL AB, Stockholm, Sweden.
[40] J. Huang, W. Liu, Z. Shi, Surface-wave attenuation zone of layered periodic structures and feasible application in ground vibration reduction, Construction and Building Materials, 141 (2017) 1-11.
[41] X. Pu, Z. Shi, Surface-wave attenuation by periodic pile barriers in layered soils, Construction and Building Materials, 180 (2018) 177-187.
)