Advertisement

Journal of Materials Science

, Volume 54, Issue 5, pp 4038–4048 | Cite as

Bandgap properties of a piezoelectric phononic crystal nanobeam based on nonlocal theory

  • Denghui Qian
Electronic materials
  • 67 Downloads

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.

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 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):141Google Scholar
  2. 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. 093508–093508-5CrossRefGoogle Scholar
  3. 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):2019CrossRefGoogle Scholar
  4. 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 431:40–53CrossRefGoogle Scholar
  5. 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):223501CrossRefGoogle Scholar
  6. 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):3319–3325CrossRefGoogle Scholar
  7. 7.
    Li L, Guo Y (2016) Analysis of longitudinal waves in rod-type piezoelectric phononic crystals. Crystals 6(4):45CrossRefGoogle Scholar
  8. 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 71:69–74CrossRefGoogle Scholar
  9. 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 70:158–171CrossRefGoogle Scholar
  10. 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):055029CrossRefGoogle Scholar
  11. 11.
    Jr EJPM, Santos JMCD (2018) Evanescent Bloch waves and complex band structure in magnetoelectroelastic phononic crystals. Mech Syst Signal Process 112:280–304CrossRefGoogle Scholar
  12. 12.
    Zhang WM, Hu KM, Peng ZK et al (2015) Tunable micro- and nanomechanical resonators. Sensors 15(10):26478–26566CrossRefGoogle Scholar
  13. 13.
    Wagner MR, Graczykowski B, Reparaz JS et al (2016) Two-dimensional phononic crystals: disorder matters. Nano Lett 16(9):5661CrossRefGoogle Scholar
  14. 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):390–403CrossRefGoogle Scholar
  15. 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 22:46–50CrossRefGoogle Scholar
  16. 16.
    Sadat SM, Wang RY (2016) Colloidal nanocrystal superlattices as phononic crystals: plane wave expansion modeling of phonon band structure. RSC Adv 6:44578–44587CrossRefGoogle Scholar
  17. 17.
    Jr EJPM, Santos JMCD (2017) Complete band gaps in nano-piezoelectric phononic crystals. Mater Res 20:15–38CrossRefGoogle Scholar
  18. 18.
    Yan Z, Jiang LY (2011) The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects. Nanotechnology 22(24):245703CrossRefGoogle Scholar
  19. 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):167–174CrossRefGoogle Scholar
  20. 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):445303CrossRefGoogle Scholar
  21. 21.
    Mindlin RD, Tiersten HF (1962) Effects of couple-stresses in linear elasticity. Arch Ration Mech Anal 11(1):415–448CrossRefGoogle Scholar
  22. 22.
    Eringen AC (1972) Nonlocal polar elastic continua. Int J Eng Sci 10(1):1–16CrossRefGoogle Scholar
  23. 23.
    Eringen AC (1983) On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys 54(9):4703–4710CrossRefGoogle Scholar
  24. 24.
    Eringen AC (2003) Nonlocal continuum field theories. Appl Mech Rev 56(2):391–398CrossRefGoogle Scholar
  25. 25.
    Ke LL, Wang YS (2012) Thermo-electric-mechanical vibration of piezoelectric nanobeams based on the nonlocal theory. Smart Mater Struct 21(2):025018CrossRefGoogle Scholar
  26. 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 68:112–122CrossRefGoogle Scholar
  27. 27.
    Arani AG, Amir S, Mozdianfard MR (2012) Nonlocal electro-thermal transverse vibration of embedded fluid-conveying DWBNNTs. J Mech Sci Technol 26(5):1455–1462CrossRefGoogle Scholar
  28. 28.
    Maraghi ZK, Arani AG, Kolahchi R et al (2013) Nonlocal vibration and instability of embedded DWBNNT conveying viscose fluid. Compos B 45(1):423–432CrossRefGoogle Scholar
  29. 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 89:316–327CrossRefGoogle Scholar
  30. 30.
    Li HB, Wang X (2016) Nonlinear dynamic characteristics of graphene/piezoelectric laminated films in sensing moving loads. Sens Actuators A 238:80–94CrossRefGoogle Scholar
  31. 31.
    Cao Y, Hou Z, Liu Y (2004) Convergence problem of plane-wave expansion method for phononic crystals. Phys Lett A 327(2–3):247–253CrossRefGoogle Scholar
  32. 32.
    Hou Z, Fu X, Liu Y (2006) Singularity of the Bloch theorem in the fluid/solid phononic crystal. Phys Rev B 73(2):024304CrossRefGoogle Scholar
  33. 33.
    Kushwaha MS, Halevi P, Dobrzynski L et al (1993) Acoustic band structure of periodic elastic composites. Phys Rev Lett 71(13):2022–2025CrossRefGoogle Scholar
  34. 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):066609CrossRefGoogle Scholar
  35. 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):2446–2457CrossRefGoogle Scholar
  36. 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):765–770CrossRefGoogle Scholar
  37. 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):3122–3125CrossRefGoogle Scholar
  38. 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):539–543CrossRefGoogle Scholar
  39. 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):1324–1332CrossRefGoogle Scholar
  40. 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):4302Google Scholar
  41. 41.
    Wang L, Bertoldi K (2012) Mechanically tunable phononic band gaps in three-dimensional periodic elastomeric structures. Int J Solids Struct 49(19–20):2881–2885CrossRefGoogle Scholar
  42. 42.
    Shi Z, Huang J (2013) Feasibility of reducing three-dimensional wave energy by introducing periodic foundations. Soil Dyn Earthq Eng 50(1):204–212CrossRefGoogle Scholar
  43. 43.
    Mencik JM (2018) A wave finite element approach for the analysis of periodic structures with cyclic symmetry in dynamic substructuring. J Sound Vib 431:441–457CrossRefGoogle Scholar
  44. 44.
    Li X, Liu Z (2005) Coupling of cavity modes and guiding modes in two-dimensional phononic crystals. Solid State Commun 133(6):397–402CrossRefGoogle Scholar
  45. 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 35:2257–2260Google Scholar
  46. 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):092301CrossRefGoogle Scholar
  47. 47.
    Romerogarcía V, Sánchezpérez JV, Garciaraffi LM (2010) Evanescent modes in sonic crystals: complex dispersion relation and supercell approximation. J Appl Phys 108(4):241Google Scholar
  48. 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):201–206Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Jiangsu Province Key Laboratory of Structure Engineering, College of Civil EngineeringSuzhou University of Science and TechnologySuzhouChina

Personalised recommendations