Bandgap properties of a piezoelectric phononic crystal nanobeam based on nonlocal theory
Source abstract
Abstract
The aim of this paper is to investigate the bandgap properties of a piezoelectric phononic crystal (PC) nanobeam with size effect by coupling the plane wave expansion method, Euler–Bernoulli beam theory and nonlocal theory. The first four orders were chosen to study the influences of thermo-electro coupling, size effect and geometric parameters on band gaps. Temperature change and external electrical voltage were chosen as the parameters capable of influencing thermo-electro coupling fields. Scale coefficient was chosen as the influencing parameters related to size effect. The lengths of PZT-4 and epoxy within a unit cell, along with the width and thickness of the PC nanobeam, were identified as influential geometric parameters. Collectively, our results are expected to be helpful for the design of piezoelectric nanobeam-based devices.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Acoustic Wave Phenomena Research · Nonlocal and gradient elasticity in micro/nano structures · Thermoelastic and Magnetoelastic Phenomena
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (48)
Show source-provided references
1. Assouar MB, Oudich M (2012) Enlargement of a locally resonant sonic band gap by using double-sides stubbed phononic plates. Appl Phys Lett 100(12):141
2. Ma J, Hou Z, Assouar BM (2014) Opening a large full phononic band gap in thin elastic plate with resonant units. J Appl Phys 115(9):pp. 093508–093508-510.1063/1.4867617 ↗
3. Shu Hai-Sheng, Shi Xiao-Na, Li Shi-Dan et al (2014) Numerical research on dynamic stress of phononic crystal rod in longitudinal wave band gap. Int J Mod Phys B 28(32):201910.1142/S0217979214502312 ↗
4. Chuang KC, Yuan ZW, Guo YQ et al (2018) A self-demodulated fiber Bragg grating for investigating impact-induced transient responses of phononic crystal beams. J Sound Vib 431:40–5310.1016/j.jsv.2018.04.035 ↗
5. Li HY, Wang Y, Ke MZ et al (2018) Acoustic manipulating of capsule-shaped particle assisted by phononic crystal plate. Appl Phys Lett 112(22):22350110.1063/1.5022704 ↗
6. Qian D, Shi Z (2016) Bandgap properties in locally resonant phononic crystal double panel structures with periodically attached spring-mass resonators. Phys Lett A 380(41):3319–332510.1016/j.physleta.2016.07.068 ↗
7. Li L, Guo Y (2016) Analysis of longitudinal waves in rod-type piezoelectric phononic crystals. Crystals 6(4):4510.3390/cryst6040045 ↗
8. Zhou C, Yi S, Chen J (2016) Tunable Lamb wave band gaps in two-dimensional magnetoelastic phononic crystal slabs by an applied external magnetostatic field. Ultrasonics 71:69–7410.1016/j.ultras.2016.05.023 ↗
9. Guo X, Wei P, Lan M et al (2016) Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with functionally graded interlayers. Ultrasonics 70:158–17110.1016/j.ultras.2016.04.025 ↗
10. Sugino C, Leadenham S, Ruzzene M et al (2017) An investigation of electroelastic bandgap formation in locally resonant piezoelectric metastructures. Smart Mater Struct 26(5):05502910.1088/1361-665X/aa6671 ↗
11. Jr EJPM, Santos JMCD (2018) Evanescent Bloch waves and complex band structure in magnetoelectroelastic phononic crystals. Mech Syst Signal Process 112:280–30410.1016/j.ymssp.2018.04.034 ↗
12. Zhang WM, Hu KM, Peng ZK et al (2015) Tunable micro- and nanomechanical resonators. Sensors 15(10):26478–2656610.3390/s151026478 ↗
13. Wagner MR, Graczykowski B, Reparaz JS et al (2016) Two-dimensional phononic crystals: disorder matters. Nano Lett 16(9):566110.1021/acs.nanolett.6b02305 ↗
14. Yan Z, Wei C, Zhang C (2017) Band structures of elastic SH waves in nanoscale multi-layered functionally graded phononic crystals with/without nonlocal interface imperfections by using a local RBF collocation method. Acta Mech Solida Sin 30(4):390–40310.1016/j.camss.2017.07.012 ↗
15. Quiroz HP, Barrera-Patiño CP, Rey-González RR et al (2016) Evidence of iridescence in TiO2, nanostructures: an approximation in plane wave expansion method. Photonics Nanostruct Fundam Appl 22:46–5010.1016/j.photonics.2016.10.003 ↗
16. Sadat SM, Wang RY (2016) Colloidal nanocrystal superlattices as phononic crystals: plane wave expansion modeling of phonon band structure. RSC Adv 6:44578–4458710.1039/C6RA03876J ↗
17. Jr EJPM, Santos JMCD (2017) Complete band gaps in nano-piezoelectric phononic crystals. Mater Res 20:15–3810.1590/1980-5373-mr-2017-0298 ↗
18. Yan Z, Jiang LY (2011) The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects. Nanotechnology 22(24):24570310.1088/0957-4484/22/24/245703 ↗
19. Liu C, Ke LL, Wang YS et al (2013) Thermo-electro-mechanical vibration of piezoelectric nanoplates based on the nonlocal theory. Compos Struct 106(12):167–17410.1016/j.compstruct.2013.05.031 ↗
20. Zhang S, Gao Y (2017) Surface effect on band structure of flexural wave propagating in magneto-elastic phononic crystal nanobeam. J Phys D Appl Phys 50(44):44530310.1088/1361-6463/aa8878 ↗
21. Mindlin RD, Tiersten HF (1962) Effects of couple-stresses in linear elasticity. Arch Ration Mech Anal 11(1):415–44810.1007/BF00253946 ↗
22. Eringen AC (1972) Nonlocal polar elastic continua. Int J Eng Sci 10(1):1–1610.1016/0020-7225(72)90070-5 ↗
23. Eringen AC (1983) On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys 54(9):4703–471010.1063/1.332803 ↗
24. Eringen AC (2003) Nonlocal continuum field theories. Appl Mech Rev 56(2):391–39810.1115/1.1553434 ↗
25. Ke LL, Wang YS (2012) Thermo-electric-mechanical vibration of piezoelectric nanobeams based on the nonlocal theory. Smart Mater Struct 21(2):02501810.1088/0964-1726/21/2/025018 ↗
26. Asemi HR, Asemi SR, Farajpour A et al (2015) Nanoscale mass detection based on vibrating piezoelectric ultrathin films under thermo-electro-mechanical loads. Physica E 68:112–12210.1016/j.physe.2014.12.025 ↗
27. Arani AG, Amir S, Mozdianfard MR (2012) Nonlocal electro-thermal transverse vibration of embedded fluid-conveying DWBNNTs. J Mech Sci Technol 26(5):1455–146210.1007/s12206-012-0307-9 ↗
28. Maraghi ZK, Arani AG, Kolahchi R et al (2013) Nonlocal vibration and instability of embedded DWBNNT conveying viscose fluid. Compos B 45(1):423–43210.1016/j.compositesb.2012.04.066 ↗
29. Ansari R, Oskouie MF, Gholami R et al (2016) Thermo-electro-mechanical vibration of postbuckled piezoelectric Timoshenko nanobeams based on the nonlocal elasticity theory. Compos Part B 89:316–32710.1016/j.compositesb.2015.12.029 ↗
30. Li HB, Wang X (2016) Nonlinear dynamic characteristics of graphene/piezoelectric laminated films in sensing moving loads. Sens Actuators A 238:80–9410.1016/j.sna.2015.12.005 ↗
31. Cao Y, Hou Z, Liu Y (2004) Convergence problem of plane-wave expansion method for phononic crystals. Phys Lett A 327(2–3):247–25310.1016/j.physleta.2004.05.030 ↗
32. Hou Z, Fu X, Liu Y (2006) Singularity of the Bloch theorem in the fluid/solid phononic crystal. Phys Rev B 73(2):02430410.1103/PhysRevB.73.024304 ↗
33. Kushwaha MS, Halevi P, Dobrzynski L et al (1993) Acoustic band structure of periodic elastic composites. Phys Rev Lett 71(13):2022–202510.1103/PhysRevLett.71.2022 ↗
34. Wu F, Liu Z, Liu Y (2004) Splitting and tuning characteristics of the point defect modes in two-dimensional phononic crystals. Phys Rev E Stat Nonlinear Soft Matter Phys 69(2):06660910.1103/PhysRevE.69.066609 ↗
35. Liu Z, Chan CT, Sheng P et al (2000) Elastic wave scattering by periodic structures of spherical objects: theory and experiment. Phys Rev B 62(4):2446–245710.1103/PhysRevB.62.2446 ↗
36. Qiu C, Liu Z, Mei J et al (2005) The layer multiple-scattering method for calculating transmission coefficients of 2D phononic crystals. Solid State Commun 134(11):765–77010.1016/j.ssc.2005.02.034 ↗
37. Sigalas MM, Garcia N (2000) Theoretical study of three dimensional elastic band gaps with the finite-difference time-domain method. J Appl Phys 87(6):3122–312510.1063/1.372308 ↗
38. Cao Y, Hou Z, Liu Y (2004) Finite difference time domain method for band-structure calculations of two-dimensional phononic crystals. Solid State Commun 132(8):539–54310.1016/j.ssc.2004.09.003 ↗
39. Wang G, Wen J, Liu Y et al (2004) Lumped-mass method for the study of band structure in two-dimensional phononic crystals. Phys Rev B 69(18):1324–133210.1103/PhysRevB.69.184302 ↗
40. Wang G, Wen J, Wen X (2005) Quasi-one-dimensional phononic crystals studied using the improved lumped-mass method: application to locally resonant beams with flexural wave band gap. Phys Rev B 71(10):4302
41. Wang L, Bertoldi K (2012) Mechanically tunable phononic band gaps in three-dimensional periodic elastomeric structures. Int J Solids Struct 49(19–20):2881–288510.1016/j.ijsolstr.2012.05.008 ↗
42. Shi Z, Huang J (2013) Feasibility of reducing three-dimensional wave energy by introducing periodic foundations. Soil Dyn Earthq Eng 50(1):204–21210.1016/j.soildyn.2013.03.009 ↗
43. Mencik JM (2018) A wave finite element approach for the analysis of periodic structures with cyclic symmetry in dynamic substructuring. J Sound Vib 431:441–45710.1016/j.jsv.2018.05.027 ↗
44. Li X, Liu Z (2005) Coupling of cavity modes and guiding modes in two-dimensional phononic crystals. Solid State Commun 133(6):397–40210.1016/j.ssc.2004.11.024 ↗
45. Wang G, Wen J, Liu Y et al (2004) Study on the calculation of elastic wave band structure in two-dimensional phononic crystals with lattice of scatters in arbitrary shape. J Funct Mater 35:2257–2260
46. Laude V, Achaoui Y, Benchabane S et al (2009) Evanescent Bloch waves and the complex band structure of phononic crystals. Phys Rev B Condens Matter 80(9):09230110.1103/PhysRevB.80.092301 ↗
47. Romerogarcía V, Sánchezpérez JV, Garciaraffi LM (2010) Evanescent modes in sonic crystals: complex dispersion relation and supercell approximation. J Appl Phys 108(4):241
48. Oudich M, Li Y, Assouar BM et al (2010) A sonic band gap based on the locally resonant phononic plates with stubs. New J Phys 12(2):201–206