In the present study, the plane wave expansion (PWE) and the stiffness matrix method (SMM) are employed to predict the transmission spectrum of piezoelectric phononic and quasi-periodic composite laminates with and without a defect layer. We propose a two-dimensional (2D) geometric system that combines two sub-models: piezoelectric phononic or quasi-periodic strips along the x-direction and periodic laminates in the z-direction. Investigations are conducted to predict the transmission coefficient variation within a high range of frequencies excitation, in quasi-periodic composite laminates and phononic composite laminates with various generation numbers. Numerical simulations show that the introduction of a non-periodic structure (nesting Fibonacci), a defect layer, as well as increasing the generation number increase the number of band gaps. Furthermore, the effect of a defect layer on the transmission spectrum of phononic or quasi-periodic composite laminates is highlighted. Finally, a parametric investigation varying the thickness of the defect layer is carried out.
SaprielJDjafari RouhaniB. Vibrations in superlattices. Surf Sci Rep1989; 10(4–5): 189–275.
2.
TamuraSIHurleyDCWolfeJP. Acoustic-phonon propagation in superlattices. Phys Rev B1988; 38(2): 1427.
3.
GaneshPUMatlackKH. Review of exploiting nonlinearity in phononic materials to enable nonlinear wave responses. Acta Mech2022; 233(1): 1–46.
4.
QiuCYLiuZYMeiJ, et al. Mode-selecting acoustic filter by using resonant tunneling of two-dimensional double phononic crystals. Appl Phys Lett2005; 87(10): 104101.
5.
KhelifADjafari-RouhaniBVasseurJO, et al. Transmittivity through straight and stublike waveguides in a two-dimensional phononic crystal. Phys Rev B2002; 65(17): 174308.
6.
LiBLiviageAJYouJH, et al. Harvesting low frequency acoustic energy using multiple PVDF beam arrays in quarter wavelength acoustic resonator. Appl Acoust2013; 74: 1271–1278.
7.
KuoN-KPiazzaG. Evidence of acoustic wave focusing in a microscale 630 MHz Aluminum Nitride phononic crystal waveguide. In: 2010 IEEE international frequency control symposium, Newport Beach, CA, 1–4 June 2010, pp. 530–533. New York: IEEE.
8.
Ghasemi BabolyMRazaABradyJ, et al. Demonstration of acoustic wave guiding and tight bending in phononic crystals. Appl Phys Lett2016; 109(18): 183504.
9.
KushwahaMSHaleviPMartinezG, et al. Theory of acoustic band structure of periodic elastic composites. Phys Rev B1994; 49(4): 2313–2322.
10.
GoffauxCVigneronJP. Theoretical study of a tunable phononic band gap system. Phys Rev B2001; 64(7): 075118.
11.
WuTTHuangZGLinS. Surface and bulk acoustic waves in two-dimensional phononic crystal consisting of materials with general anisotropy. Phys Rev B2004; 69(9): 1–10.
12.
LiYHouZOudichM, et al. Analysis of surface acoustic wave propagation in a two-dimensional phononic crystal. J Appl Phys2012; 112(2): 023524.
13.
WuTTHsuZCHuangZG. Band gaps and the electromechanical coupling coefficient of a surface acoustic wave in a two-dimensional piezoelectric phononic crystal. Phys Rev B2005; 71: 064303.
14.
QuotaneIEl BoudoutiEHDjafari-RouhaniB, et al. Bulk and surface acoustic waves in solid–fluid Fibonacci layered materials. Ultrasonics2015; 61: 40–51.
15.
BacigalupoADe BellisLMVastaM. Design of tunable hierarchical waveguides based on Fibonacci-like microstructure. J Mech Sci2022; 224: 107280.
16.
MoriniLGeiM. Waves in one-dimensional quasicrystalline structures: dynamical trace mapping, scaling and self-similarity of the spectrum. J Mech Phys Solids2018; 119: 83–103.
17.
ChenJQinBChanHLW. Engineering band gap forming using the combination of periodic and Fibonacci quasi-periodic one-dimensional composite thin plates. Solid State Commun2008; 146: 491–494.
18.
WuMLWuLYYangWP, et al. Elastic wave band gaps of one-dimensional phononic crystals with functionally graded materials. Smart Mater Struct2009; 18(11): 115013.
19.
BianZYangSZhouX, et al. Band gap manipulation of viscoelastic functionally graded phononic crystal. Nanotechnol Rev2020; 9(1): 515–523.
20.
MkaoirMKetataHNjehA. Lamb waves propagating in one-dimensional phononic composite and nesting Fibonacci piezoelectric superlattices plate coated on a uniform substrate. Mech Adv Mater Struct2022; 29(25): 3623–3632.
21.
WengRZhangYYangZK, et al. Study on the transmission properties of periodical and quasi-periodical phononic crystal in elastic wave. Modern Phys Lett B2015; 29(34): 1550229.
22.
MkaoirMEzzinHKetataH, et al. Study of the transmission properties of piezoelectric/piezomagnetic phononic composite laminates. Arch Appl Mech2023; 93: 2273–2285.
23.
GarusSSochackiW. One dimensional phononic FDTD algorithm and transfer matrix method implementation for Severin aperiodic multilayer. J Appl Math Comput Mech2017; 16: 17–27.
24.
WrightDWCobboldRSC. Acoustic wave transmission in time-varying phononic crystals. Smart Mater Struct2008; 18(1): 015008.
25.
WangYSongWSunE, et al. Tunable pass band in one-dimensional phononic crystal containing a piezoelectric 0.62Pb(Mg1/3Nb2/3)O3–0.38PbTiO3 single crystal defect layer. Physica E2014; 60: 37–41.
26.
ArafaHAMehaneyA. Phononic crystals with one-dimensional defect as sensor materials. Indian J Phys2017; 91: 1021–1028.
27.
CuiHGaoQLiX, et al. A Novel method for Transient Heat Conduction in a quasi-periodic structure with nonlinear defects. J Heat Transf2020; 142(12): 124502.
28.
AlyAHNagatyAMehaneyA. Thermal properties of one dimensional piezoelectric phononic crystal. Eur Phys J B2018; 91(10): 251.
29.
MehaneyAElsayedHA. Hydrostatic pressure effects on a one-dimensional defective phononic crystal comprising a polymer material. Solid State Commun2020; 322: 114054.
30.
YanDLiuRZhouJ, et al. Influences of defects on the propagation of transverse waves in periodic piezoelectric laminate structure with nanoscaled layers. Thin-Walled Struct2022; 179: 109567.
31.
LiuCXYuG-L. Predicting the dispersion relations of one-dimensional phononic crystals by neural networks. Sci Rep2019; 9(1): 1–10.
32.
FomenkoSIGolubMVDoroshenkoOV, et al. An advanced boundary integral equation method for wave propagation analysis in a layered piezoelectric phononic crystal with a crack or an electrode. J Comput Phys2021; 447: 110669.
33.
LiFLZhangCWangYS. Band structure analysis of phononic crystals with imperfect interface layers by the BEM. Eng Anal Bound Elem2021; 131: 240–257.
YanDJChenALWangYS, et al. Propagation of guided elastic waves in nanoscale layered periodic piezoelectric composites. Eur J Mech A-solid2017; 66: 158–167.
36.
ChenALTianLZWangYS. Band structure properties of elastic waves propagating in the nanoscaled nearly periodic layered phononic crystals. Acta Mech Solida Sinica2017; 30: 113–122.
37.
LiCADong-JiaYYue-ShengWY, et al. In-plane elastic wave propagation in nanoscale periodic piezoelectric/piezomagnetic laminates. Int J Mech Sci2019; 153: 416–429.
38.
EconomouENSigalasM. Stop bands for elastic waves in periodic composite materials. J Acoust Soc Am1994; 95(4): 1734–1740.
39.
ZhilinHFuXLiuY. Acoustic wave in a two-dimensional composite medium with anisotropic inclusions. Phys Lett A2003; 317(1–2): 127–134.
40.
EzzinHDasRZhenghuaQ, et al. Energy reflection and transmission characteristics of acoustic waves in a functionally graded piezoelectric plate immersed into non-viscous fluid. J Sound Vib2022; 535: 117139.
41.
RoyerDDieulesaintE.
Elastic waves in solids I: free and guided propagation. Berlin and Heidelberg: Springer Science & Business Media, 1999.
42.
FarjallahHHassibaKGhozlenMHB. Application of plane wave expansion and stiffness matrix methods to study transmission properties and guided mode of phononic plates. Wave Motion2016; 64: 68–78.
43.
WangLRokhlinSL. A compliance/stiffness matrix formulation of general Green’s function and effective permittivity for piezoelectric multilayers. IEEE Trans Ultrason Ferroelectr Freq Control2004; 51(4): 453–463.
44.
ZaitsevBDKuznetsovaIE. The energy density and power flow of acoustic waves propagating in piezoelectric materials. IEEE Trans Ultrason Ferroelectr Freq Control2003; 50(12): 1762–1765.
45.
EzzinHWangBQianZ. Propagation behavior of ultrasonic Love waves in functionally graded piezoelectric-piezomagnetic materials with exponential variation. Mech Mater2020; 148: 103492.
