Electro-mechanical coupling wave propagating in a locally resonant piezoelectric/elastic phononic crystal nanobeam with surface effects

doi:10.1007/s10483-020-2586-5

Applied Mathematics and Mechanics (English Edition) ›› 2020, Vol. 41 ›› Issue (3): 425-438.doi: https://doi.org/10.1007/s10483-020-2586-5

Electro-mechanical coupling wave propagating in a locally resonant piezoelectric/elastic phononic crystal nanobeam with surface effects

Denghui QIAN

Jiangsu Province Key Laboratory of Structure Engineering, College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, Jiangsu Province, China

收稿日期:2019-09-09 修回日期:2019-12-09 出版日期:2020-03-01 发布日期:2020-02-17
通讯作者: Denghui QIAN E-mail:dhqian@usts.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (No. 11847009) and the Natural Science Foundation of Suzhou University of Science and Technology (No. XKQ2018007)

Electro-mechanical coupling wave propagating in a locally resonant piezoelectric/elastic phononic crystal nanobeam with surface effects

Denghui QIAN

Jiangsu Province Key Laboratory of Structure Engineering, College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, Jiangsu Province, China

Received:2019-09-09 Revised:2019-12-09 Online:2020-03-01 Published:2020-02-17
Contact: Denghui QIAN E-mail:dhqian@usts.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11847009) and the Natural Science Foundation of Suzhou University of Science and Technology (No. XKQ2018007)

摘要/Abstract

摘要： The model of a "spring-mass" resonator periodically attached to a piezoelectric/elastic phononic crystal (PC) nanobeam with surface effects is proposed, and the corresponding calculation method of the band structures is formulized and displayed by introducing the Euler beam theory and the surface piezoelectricity theory to the plane wave expansion (PWE) method. In order to reveal the unique wave propagation characteristics of such a model, the band structures of locally resonant (LR) elastic PC Euler nanobeams with and without resonators, the band structures of LR piezoelectric PC Euler nanobeams with and without resonators, as well as the band structures of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on PZT-4, with resonators attached on epoxy, and without resonators are compared. The results demonstrate that adding resonators indeed plays an active role in opening and widening band gaps. Moreover, the influence rules of different parameters on the band gaps of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on epoxy are discussed, which will play an active role in the further realization of active control of wave propagations.

关键词: locally resonant (LR) piezoelectric/elastic phononic crystal (PC) nanobeam, surface effect, plane wave expansion (PWE) method, spring-mass resonator

Abstract: The model of a "spring-mass" resonator periodically attached to a piezoelectric/elastic phononic crystal (PC) nanobeam with surface effects is proposed, and the corresponding calculation method of the band structures is formulized and displayed by introducing the Euler beam theory and the surface piezoelectricity theory to the plane wave expansion (PWE) method. In order to reveal the unique wave propagation characteristics of such a model, the band structures of locally resonant (LR) elastic PC Euler nanobeams with and without resonators, the band structures of LR piezoelectric PC Euler nanobeams with and without resonators, as well as the band structures of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on PZT-4, with resonators attached on epoxy, and without resonators are compared. The results demonstrate that adding resonators indeed plays an active role in opening and widening band gaps. Moreover, the influence rules of different parameters on the band gaps of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on epoxy are discussed, which will play an active role in the further realization of active control of wave propagations.

Key words: locally resonant (LR) piezoelectric/elastic phononic crystal (PC) nanobeam, surface effect, plane wave expansion (PWE) method, spring-mass resonator

中图分类号:

Denghui QIAN. Electro-mechanical coupling wave propagating in a locally resonant piezoelectric/elastic phononic crystal nanobeam with surface effects[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(3): 425-438.

参考文献 28

[1]	ALMUSALLAM, A., LUO, Z. H., KOMOLAFE, A., YANG, K., ROBINSON, A., TORAH, R., and BEEBY, S. Flexible piezoelectric nano-composite films for kinetic energy harvesting from textiles. Nano Energy, 33, 146-156(2017)
[2]	LI, Y. D., BAO, R., and CHEN, W. Buckling of a piezoelectric nanobeam with interfacial imperfection and van der Waals force:is nonlocal effect really always dominant? Composite Structures, 194, 357-364(2018)
[3]	ZHANG, Y. H., HONG, J. W., LIU, B., and FANG, D. N. Strain effect on ferroelectric behaviors of BaTiO3 nanowires:a molecular dynamics study. Nanotechnology, 21(1), 015701(2010)
[4]	YANG, Y., GUO, W., WANG, X. Q., WANG, Z. Z., QI, J. J., and ZHANG, Y. Size dependence of dielectric constant in a single pencil-like ZnO nanowire. Nano Letters, 12(4), 1919-1922(2012)
[5]	AREFI, M. Surface effect and non-local elasticity in wave propagation of functionally graded piezoelectric nano-rod excited to applied voltage. Applied Mathematics and Mechanics (English Edition), 37(3), 289-302(2016) https://doi.org/10.1007/s10483-016-2039-6
[6]	ZHOU, Y. R., YANG, X., PAN, D. M., and WANG, B. L. Improved incorporation of strain gradient elasticity in the flexoelectricity based energy harvesting from nanobeams. Physica E:Low-dimensional Systems and Nanostructures, 98, 148-158(2018)
[7]	ZENG, S., WANG, B. L., and WANG, K. F. Static stability analysis of nanoscale piezoelectric shells with flexoelectric effect based on couple stress theory. Microsystem Technologies, 24(7), 2957-2967(2018)
[8]	GURTIN, M. E. and MURDOCH, A. I. A continuum theory of elastic material surfaces. Archive for Rational Mechanics & Analysis, 57(4), 291-323(1975)
[9]	MILLER, R. E. and SHENOY, V. B. Size-dependent elastic properties of nanosized structural elements. Nanotechnology, 11(3), 139-147(2000)
[10]	HUANG, G. Y. and YU, S. W. Effect of surface piezoelectricity on the electromechanical behaviour of a piezoelectric ring. Physica Status Solidi, 243(4), 22-24(2006)
[11]	XU, X. J., DENG, Z. C., and WANG, B. Closed solutions for the electromechanical bending and vibration of thick piezoelectric nanobeams with surface effects. Journal of Physics D:Applied Physics, 46(40), 405302(2013)
[12]	WANG, K. F. and WANG, B. L. Nonlinear fracture mechanics analysis of nano-scale piezoelectric double cantilever beam specimens with surface effect. European Journal of Mechanics A/Solids, 56, 12-18(2016)
[13]	YUE, Y. M., XU, K. Y., ZHANG, X. D., and WANG, W. J. Effect of surface stress and surface-induced stress on behavior of piezoelectric nanobeam. Applied Mathematics and Mechanics (English Edition), 39(7), 953-966(2018) https://doi.org/10.1007/s10483-018-2346-8
[14]	FANG, X. Q., ZHU, C. S., LIU, J. X., and LIU, X. L. Surface energy effect on free vibration of nano-sized piezoelectric double-shell structures. Physica B:Condensed Matter, 529, 41-56(2018)
[15]	MIRANDA, E. J. P., JR. and DOS SANTOS, J. M. C. Complete band gaps in nanopiezoelectricphononic crystals. Materials Research, 20, 15-38(2017)
[16]	YAN, Z., WEI, C., and ZHANG, C. Band structure calculation of SH waves in nanoscale multilayered piezoelectric phononic crystals using radial basis function method with consideration of nonlocal interface effects. Ultrasonics, 73, 169-180(2017)
[17]	QIAN, D. H. Bandgap properties of a piezoelectric phononic crystal nanobeam based on nonlocal theory. Journal of Materials Science, 54(5), 4038-4048(2019)
[18]	WANG, Y. Z., LI, F. M., HUANG, W. H., and WANG, Y. S. Effects of inclusion shapes on the band gaps in two-dimensional piezoelectric phononic crystals. Journal of Physics:Condensed Matter, 19(49), 496204(2007)
[19]	WANG, Y. Z., LI, F. M., HUANG, W. H., and WANG, Y. S. The propagation and localization of Rayleigh waves in disordered piezoelectric phononic crystals. Journal of the Mechanics and Physics of Solids, 56(4), 1578-1590(2008)
[20]	WANG, Y. Z., LI, F. M., KISHIMOTO, K., WANG, Y. S., and HUANG, W. H. Band gaps of elastic waves in three-dimensional piezoelectric phononic crystals with initial stress. European Journal of Mechanics A/Solids, 29(2), 182-189(2010)
[21]	JIANG, S., DAI, L. X., CHEN, H., HU, H. P., JIANG, W., and CHEN, X. D. Folding beam-type piezoelectric phononic crystal with low-frequency and broad band gap. Applied Mathematics and Mechanics (English Edition), 38(3), 411-422(2017) https://doi.org/10.1007/s10483-017-2171-7
[22]	NAGATY, A., MEHANEY, A., and ALY, A. H. Influence of temperature on the properties of one-dimensional piezoelectric phononic crystals. Chinese Physics B, 27(9), 346-349(2018)
[23]	YAN, X. J., LIU, X. P., NI, X., CHEN, Z. G., LU, M. H., and CHEN, Y. F. Reduce thermal conductivity by forming a nano-phononic crystal on a Si slab. Europhysics Letters, 106(5), 56002(2014)
[24]	TRAVAGLIATI, M., NARDI, D., GIANNETTI, C., GUSEV, V., PINGUE, P., PIAZZA, V., FERRINI, G., and BANFI, F. Interface nano-confined acoustic waves in polymeric surface phononic crystals. Applied Physics Letters, 106(2), 021906(2015)
[25]	XIAO, Y., WEN, J., and WEN, X. Flexural wave band gaps in locally resonant thin plates with periodically attached spring-mass resonators. Journal of Physics D:Applied Physics, 45(19), 195401(2012)
[26]	QIAN, D. H. and SHI, Z. Y. Bandgap properties in locally resonant phononic crystal double panel structures with periodically attached spring-mass resonators. Physics Letters A, 380(41), 3319-3325(2016)
[27]	QIAN, D. H. Bandgap properties of a piezoelectric phononic crystal nanobeam with surface effect. Journal of Applied Physics, 124(5), 055101(2018)
[28]	QIAN, D. H., SHI, Z. Y., NING, C. W., and WANG, J. C. Nonlinear bandgap properties in a nonlocal piezoelectric phononic crystal nanobeam. Physics Letters A, 383(25), 3101-3107(2019)

Electro-mechanical coupling wave propagating in a locally resonant piezoelectric/elastic phononic crystal nanobeam with surface effects

Electro-mechanical coupling wave propagating in a locally resonant piezoelectric/elastic phononic crystal nanobeam with surface effects

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