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

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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, band structures of locally resonant (LR) elastic PC Euler nanobeams with and without resonators, band structures of LR piezoelectric PC Euler nanobeams with and without resonators, as well as 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. Results demonstrate that adding resonators indeed plays an active role in opening and widening band gaps. Moreover, the influence rules of different parameters on 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.

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Author information

Correspondence to Denghui Qian.

Additional information

Project supported by the National Natural Science Foundation of China (No. 11847009) and Natural Science Foundation of Suzhou University of Science and Technology (No. XKQ2018007)

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Qian, D. Electro-mechanical coupling wave propagating in a locally resonant piezoelectric/elastic phononic crystal nanobeam with surface effects. Appl. Math. Mech.-Engl. Ed. (2020) doi:10.1007/s10483-020-2586-5

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Key words

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

Chinese Library Classification

  • O175.9
  • O34
  • O735

2010 Mathematics Subject Classification

  • 15A18
  • 74J10
  • 78M16