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Indexed by:
Journal paper
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First Author:
Haoyu Xu
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Correspondence Author:
Hongping Hu
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Co-author:
Weiwei Wang,Ningdong Hu,Mingge Yao
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Journal:
Applied Mathematical Modelling
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Included Journals:
SCI
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Affiliation of Author(s):
Huazhong University of Science and Technology
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Discipline:
Engineering
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First-Level Discipline:
Mechanics
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Funded by:
Shanghai Aerospace Science and Technology Innovation Fund (No. SAST2023-042), and National Natural S
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Document Type:
J
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Volume:
146
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Page Number:
116172
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ISSN No.:
0307-904X
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Key Words:
Nonlocal strain gradient theory
Method of reverberation-ray matrix
Band structures
Size effect
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DOI number:
10.1016/j.apm.2025.116172
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Date of Publication:
2025-04-29
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Impact Factor:
4.4
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Abstract:
With the proposal of the high-order nonlocal theories for studying size effect on nano structure, due to the poor numerical convergence, the traditional transfer matrix method (TMM) can no
longer meet its requirements in the research of the size effect on nano phononic crystals (PnCs), which leads to the lack of research on nano PnCs. To overcome the shortcoming, a theoretical
model is established for the analysis of size effect on the PnCs based on nonlocal strain gradient theory (NSGT). The method of reverberation-ray matrix (MRRM) is first introduced to obtain the
analytical solution of size effect on band structures of the PnCs. Compared with TMM, MRRM shows excellent numerical stability in studying size effect on both finite and infinite nano PnCs with a wide parameter range, which is verified by finite element method (FEM). Numerical results reveal that softening effect will reduce the frequency, while the stiffening effect will increase the frequency, thereby leading to a complex size effect on the band structure and wave attenuation. The different mechanisms of softening and hardening effects on the bandwidth and wave attenuation of the first bandgap are investigated. The stiffening effect first widens the bandwidth and enhances wave attenuation at lower intensities, while narrowing the bandwidth and weakening wave attenuation at higher intensities. However, the softening effect only narrows the bandwidth and enhances wave attenuation. There exist specific optimal nonlocal parameters that maximize both bandwidth and wave attenuation. This study paves the way for investigating the
size effect on nano PnCs with a numerical stable calculation method, and provides theoretical guidance for the design and application of nano PnCs.
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Links to published journals:
