Studies on calculation method and bandgap properties of a nonlocal piezoelectric phononic crystal nanoplate

Xiang-Rong, Song; Qian, Denghui; Qi, Yi

doi:10.1080/00150193.2020.1839264

Cited by 8 publications

(8 citation statements)

References 23 publications

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“…Based on the literature [13,30] and the derivation of a series of formulas, the governing equations for PC plate can be written uniformly in the following form:…”

Section: Frequency Band Structure Obtained By Fe/pde Methodsmentioning

confidence: 99%

“…)is the bending displacement in the z-direction, L is the generic term, its meaning depends on the type of structure, see table 1 for details. m n p q , , is the material component coefficient [13,30], which is calculated as shown in table 2. Where, w is the frequency, l h, r = r is the density of the material, s ,…”

Section: Frequency Band Structure Obtained By Fe/pde Methodsmentioning

confidence: 99%

“…At this point, equation (1) can be successfully converted to a second-order equation. The final form of the solution of equation (1) in COMSOL is shown in equation (13). It is worth noting that when solving equation (13) in COMSOL's PDE module, the order of partial derivatives can have a significant impact on the results.…”

Section: Structure Type Lmentioning

confidence: 99%

“…Provides an option for engineering UHF vibration damping needs. Qian [13] introduced the non-local elastic theory and Kirchhoff plate theory to the PWE method, and the band structure of a non-local piezoelectric PC nanoplate is calculated. A complete band gap with magnitude order gigahertz (GHz) is opened.…”

Section: Introductionmentioning

confidence: 99%

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FE/PDE: a novel approach applied to PC plate structure with multi-scale and multi-physics field coupling

Qian,

Liu

2024

Phys. Scr.

Self Cite

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For the more straightforward and more efficient solution of phononic crystal (PC) plate frequency band structure, transmission curve, and vibration mode, in this paper, related theories based on spatial Fourier series expansions, combined with Bloch’s theorem, a novel approach to solve the structural governing equations of PC plate is proposed by using the partial differential equations (PDE) module in the finite element software COMSOL. It is named the FE/PDE (Finite element and partial differential equations) method. The method’s accuracy is verified by comparing the results with those obtained from the traditional method. Systematic elucidation of the application of the method to probe the properties of multi-scale, multi-physics field coupled PC plate. In order to demonstrate the flexibility and scientific validity of the method, a novel nano-piezoelectric PC plate structure is proposed and solved. The method is simple, computationally efficient, and applicable, and provides a new method for investigating the properties of PC plates.

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“…Based on the literature [13,30] and the derivation of a series of formulas, the governing equations for PC plate can be written uniformly in the following form:…”

Section: Frequency Band Structure Obtained By Fe/pde Methodsmentioning

confidence: 99%

Section: Frequency Band Structure Obtained By Fe/pde Methodsmentioning

confidence: 99%

Section: Structure Type Lmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

FE/PDE: a novel approach applied to PC plate structure with multi-scale and multi-physics field coupling

Qian,

Liu

2024

Phys. Scr.

Self Cite

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show abstract

“…These theories and their extended versions are widely applied to predict the bandgap at the micron and nanometer scales. For example, Qian et al [34] and Song et al [35] examined the effects of external electric and temperature fields on the bandgap for piezoelectric PC nanobeams and nanoplates based on the nonlocal theory. Qian [36] also studied the surface effect on bandgaps in a PC nanobeam.…”

Section: Introductionmentioning

confidence: 99%

Tunable Bandgaps in Phononic Crystal Microbeams Based on Microstructure, Piezo and Temperature Effects

Hong

Zhang

et al. 2021

Crystals

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A new model of non-classical phononic crystal (PC) microbeam for the elastic wave bandgap generation is provided, incorporating microstructure, piezomagnetism, piezoelectricity and temperature effects. The wave equation of a general magneto–electro–elastic (MEE) phononic crystal microbeam is derived, which recovers piezoelectric- and piezomagnetic-based counterparts as special cases. The piezomagnetic and piezoelectric materials are periodically combined to construct the PC microbeam and corresponding bandgaps are obtained by using the plane wave expansion (PWE) method. The effects of the piezomagnetism, piezoelectricity, microstructure, geometrical parameters and applied multi-fields (e.g., external electric potential, external magnetic potential, temperature change) on the bandgaps are discussed. The numerical results reveal that the bandgap frequency is raised with the presence of piezo and microstructure effects. In addition, the geometry parameters play an important role on the bandgap. Furthermore, large bandgaps can be realized by adjusting the external electric and magnetic potentials at micron scale, and lower bandgap frequency can be realized through the temperature rise at all length scales.

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Complete guided wave in piezoelectric nanoplates: A nonlocal stress expansion polynomial method

Liu

Zhang

et al. 2022

European Journal of Mechanics - A/Solids

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Studies on calculation method and bandgap properties of a nonlocal piezoelectric phononic crystal nanoplate

Cited by 8 publications

References 23 publications

FE/PDE: a novel approach applied to PC plate structure with multi-scale and multi-physics field coupling

FE/PDE: a novel approach applied to PC plate structure with multi-scale and multi-physics field coupling

Tunable Bandgaps in Phononic Crystal Microbeams Based on Microstructure, Piezo and Temperature Effects

Complete guided wave in piezoelectric nanoplates: A nonlocal stress expansion polynomial method

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