A non-classical couple stress based Mindlin plate finite element framework for tuning band gaps of periodic composite micro plates

Xia, Zixu; Zhang, Gongye; Yu, Chan; Gu, Shuitao

doi:10.1016/j.jsv.2022.116889

Cited by 11 publications

(5 citation statements)

References 44 publications

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“…According to the Bloch-Floquet theorem [43], the displacement field of the unit cell can be expressed as plane waves modulated by a periodic function.…”

Section: Data Availability Statementmentioning

confidence: 99%

Design of phononic crystals using superposition of defect and gradient-index for enhanced wave focusing

Shen,

Cong,

et al. 2024

Smart Mater. Struct.

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This paper introduces a novel design strategy for phononic crystals (PnCs) that significantly enhances their wave amplification and focusing capabilities, making them highly suitable for energy harvesting applications. The strategy is based on the combination of two distinct wave tuning techniques: defect PnCs implementation and gradient-index (GRIN) structure designs. The two techniques are based on different mechanisms and are commonly considered independently for wave manipulation applications. In particular, defect PnCs incorporate structural or material irregularities within periodic PnCs, enabling waves of certain frequencies, typically blocked by the bandgap, to pass through and emerge with amplified amplitude at the defect location. In contrast, the gradient-index technique utilizes gradient structures that induce refractive effect to the wave propagation, focusing the wave at a pre-determined location. The PnC design strategy that we propose combines the wave amplifying effect of defect PnCs in conjunction with the wave focusing effect of the gradient-index mechanism. This combination leads to substantial performance improvement, with enhancement factors of 2.6 and 4.1, in comparison with individually implemented defect or gradient models, respectively. These results open up new possibilities for the development of PnCs with the goal of tuning wave propagations for optimized vibration energy harvesters.

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“…According to the Bloch-Floquet theorem [43], the displacement field of the unit cell can be expressed as plane waves modulated by a periodic function.…”

Section: Data Availability Statementmentioning

confidence: 99%

Design of phononic crystals using superposition of defect and gradient-index for enhanced wave focusing

Shen,

Cong,

et al. 2024

Smart Mater. Struct.

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“…This theory involves only one additional material parameter and can effectively capture the size-dependent effects while being more accessible and easier to interpret in practice. Furthermore, the modified couple stress theory has been widely applied in studies of wave propagation and its control [16], including through temporal, frequency responses, and bandgap analysis, both using analytical [17] and numerical [18] methods. Therefore, we consider the modified couple stress theory to be a favourable compromise to model the microstructure effects with reasonable computational effort, making it well-suited for topology optimisation calculations.…”

Section: Introductionmentioning

confidence: 99%

Topology optimisation for vibration bandgaps of periodic composite plates using the modified couple stress continuum

Cong,

Xia,

et al. 2024

Mathematics and Mechanics of Solids

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We propose a topology optimisation approach that can effectively account for the size effect of periodic composite plates to determine the optimal material distribution for achieving the largest bandgap width. The approach is based on the modified couple stress continuum and uses the relative bandgap width as the objective function, with volume constraints defined as the constraint function. The material properties are represented by the solid isotropic material with penalisation (SIMP) interpolation model, and the optimality criteria (OC) algorithm is employed to update the design variables. To address the significant size effect of the microplate structure, we use the modified couple stress continuum to model the dynamic behaviour of the unit cell. The Melosh–Zienkiewicz–Cheung (MZC) finite element is employed to ensure nodal [Formula: see text] continuity and achieve high-order elasticity with respect to inter-element continuity. Our results demonstrate that the proposed topology optimisation methodology is capable of effectively designing optimal unit cell configurations that account for size effect and significantly improve the bandgap width. We also investigate the impact of thickness and volume limitations on the optimised unit cell configuration. The obtained results suggest that the proposed topology optimisation framework is a promising approach for designing unit cell geometries with the account for size effect.

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“…Zaki et al [24] designed a greenhouse gas sensor with a size of 2 µm, while Almawgani et al [25] designed a cadmium bromide sensor with a unit cell dimension of 0.2 µm. At this scale, the structure will display apparent size effects [26][27][28], making the calculation of bandgap and resonant frequency using classical elasticity theory prone to significant inaccuracies. Consequently, it is vital to consider the microstructure effect and apply a more sophisticated theory that accounts for size effects during calculations.…”

Section: Introductionmentioning

confidence: 99%

Size effects on a one-dimensional defective phononic crystal sensor

Shu,

Zhang,

Cong

et al. 2023

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The influence of size effects on one-dimensional defective phononic crystal sensors based on simplified strain gradient elasticity theory is studied in this paper. Phononic crystals have been widely used in high-sensitivity gas and liquid sensors by introducing defects to disrupt the perfect phononic crystal modes. In comparison with classical elasticity theory, the simplified strain gradient elasticity theory includes two microstructure-related material parameters that can accurately reflect the size effects of the structure. In this paper, the stiffness matrix method was used to calculate the transmission coefficients of the proposed model, avoiding the numerical instability of the transfer matrix method. The results show that the size effects at the microscale affect the perfect phononic crystal bandgap's frequency range, and the microstructure constants impress the resonant frequency while detecting liquids. Consequently, the accuracy of the sensor is reduced. These findings provide a theoretical basis for designing microscale phononic crystal sensors.

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A non-classical couple stress based Mindlin plate finite element framework for tuning band gaps of periodic composite micro plates

Cited by 11 publications

References 44 publications

Design of phononic crystals using superposition of defect and gradient-index for enhanced wave focusing

Design of phononic crystals using superposition of defect and gradient-index for enhanced wave focusing

Topology optimisation for vibration bandgaps of periodic composite plates using the modified couple stress continuum

Size effects on a one-dimensional defective phononic crystal sensor

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