Dispersion relations of elastic waves in three-dimensional cubical piezoelectric phononic crystal with initial stresses and mechanically and dielectrically imperfect interfaces

J.O. Vasseur, P.A. Deymier, B. Chenni, B. Djafari-Rouhani, L. Dobrzynski, D. Prevost, Experimental and theoretical evidence for the existence of absolute acoustic band gaps in two-dimensional solid phononic crystals, Phys. Rev. Lett. 86 (2001) 3012–3015. S. Benchabane, A. Khelif, J.Y. Rauch, L. Robert, V. Laude, Evidence for complete surface wave band gap in a piezoelectric phononic crystal, Phys. Rev. E 73 (2006), 065601(R). F. Wu, H. Zhong, S. Zhong, Z. Liu, Y. Liu, Localized states of acoustic waves in three-dimensional periodic composites with point defects, Eur. Phys. J. B 34 (2003) 265–268. Zhang, 2003, The optimum elastic wave band gaps in three dimensional phononic crystals with local resonance, Eur. Phys. J. B, 42, 477, 10.1140/epjb/e2005-00005-y Zhang, 2003, Elastic wave band gaps for three-dimensional phononic crystals with two structural units, Phys. Lett. A, 313, 455, 10.1016/S0375-9601(03)00807-7 Zhao, 2007, Absorptive properties of three-dimensional phononic crystal, J. Sound Vib., 303, 185, 10.1016/j.jsv.2007.01.004 Wang, 2010, Band gaps of elastic waves in three-dimensional piezoelectric phononic crystals with initial stress, Eur. J. Mech. A Solid, 29, 182, 10.1016/j.euromechsol.2009.09.005 Ma, 2013, Effects of material parameters on elastic band gaps of three-dimensional solid phononic crystals, Phys. Scripta, 87, 10.1088/0031-8949/87/05/055604 Kutsenko, 2013, On the quasistatic effective elastic moduli for elastic waves in three-dimensional phononic crystals, J. Mech. Phys. Solids., 61, 2260, 10.1016/j.jmps.2013.06.003 Yuan, 2013, On the coupling of resonance and Bragg scattering effects in three-dimensional locally resonant sonic materials, Ultrasonics, 53, 1332, 10.1016/j.ultras.2013.03.019 H. Salehi, M. Aryadoust, M.Z. Shoushtari, Investigation the effect of lattice angle on the band gap width in 3D phononic crystals with rhombohedral(I) lattice, Appl. Phys. A 116 (2014) 69–77. Aryadoust, 2014, Investigation the effect of lattice angle on the band structure in 3D phononic crystals with rhombohedral(II) lattice, Appl. Phys. A, 117, 2037, 10.1007/s00339-014-8614-x Delpero, 2016, Structural engineering of three-dimensional phononic crystals, J. Sound Vib, 363, 156, 10.1016/j.jsv.2015.10.033 Lee, 2017, Fundamentals and applications of 3D printing for novel materials, Appl. Mater. Today, 7, 120, 10.1016/j.apmt.2017.02.004 Yang, 2016, Thermoelectric properties of nanoscale three dimensional Si phononic crystals, Int. J. Heat. Mass. Tran., 99, 102, 10.1016/j.ijheatmasstransfer.2016.03.096 Z. Qian, F. Jin, K. Kishimoto, Z. Wang, Effect of initial stress on the propagation behavior of SH-waves in multilayered piezoelectric composite structures, Sensor. Actuat. A 112 (2004) 368–375. Y. Wang, F. Li, K. Kishimoto, Y. Wang, W. Huang, Wave localization in randomly disordered periodic piezoelectric rods with initial stress, Acta. Mech. Solida. Sin. 21 (2008) 529–535. Abd-alla, 2009, Reflection and refraction of plane quasilongitudinal waves at an interface of two piezoelectric media under initial stresses, Arch. Appl. Mech., 79, 843, 10.1007/s00419-008-0257-y Guo, 2016, Dispersion relations of elastic waves in one-dimensional piezoelectric phononic crystal with initial stresses, Int. J. Mech. Sci., 106, 231, 10.1016/j.ijmecsci.2015.12.020 M. Zheng, P. Wei, Band-gaps of elastic waves in 1-D phononic crystals with imperfect interfaces, Int. J. Min. Met. Mater. 16 (2009) 608–614. W.H. Sun, G.L. Ju, J.W. Pan, Y.D. Li, Effects of the imperfect interface and piezoelectric/piezomagnetic stiffening on the SH wave in a multiferroic composite, Ultrasonics 51 (2011), 831–838. M. Lan, P. Wei, Laminated piezoelectric phononic crystal with imperfect interfaces, J. Appl. Phys. 111 (2012) 013505. Guo, 2015, Influences of mechanically and dielectrically imperfect interfaces on the reflection and transmission waves between two piezoelectric half spaces, Int. J. Solids. Struct., 63, 184, 10.1016/j.ijsolstr.2015.02.050 M. Vaezi, H. Seitz, S. Yang, A review on 3D micro-additive manufacturing technologies, Int. J. Adv. Manuf. Technol. 67 (2013) 1721–1754. F. Lucklum, M.J. Vellekoop, Rapid prototyping of 3D phononic crystals using high-resolution stereolithography fabrication, Proced. Eng. 120 (2015) 1095–1098. K.I. Lee, S.W. Yoon, Acoustic band structures and time reversal of elastic waves in two- and three-dimensional phononic crystals, J. Korean Phys. Soc. 68 (2016) 398–402. Wang, 2016, Band structures in Sierpinski triangle fractal porous phononic crystals, Phys. B, 498, 33, 10.1016/j.physb.2016.06.018 Guo, 2018, Dispersion relations of elastic waves in two-dimensional tessellated piezoelectric phononic crystals, Appl. Math. Model., 56, 65, 10.1016/j.apm.2017.11.037 J.O. Vasseur, A.C. Hladky-Hennion, B. Djafari-Rouhani, F. Duval, B. Dubus, Y. Pennec, Waveguiding in two-dimensional piezoelectric phononic crystal plates, J. Appl. Phys. 101 (2007) 114904. Ji, 2016, Development of an acoustic filter for parametric loudspeaker using phononic crystals, Ultrasonics, 67, 160, 10.1016/j.ultras.2016.01.013 Auld, 1990