Composite Structures最新文献_第5页

Experimental investigation of the behavior of UHPCFST under repeated eccentric compression 对 UHPCFST 在反复偏心压缩下的行为进行实验研究

IF 6.3 2区材料科学 Q1 MATERIALS SCIENCE, COMPOSITES

Composite Structures

Pub Date : 2024-10-21 DOI: 10.1016/j.compstruct.2024.118661

Chunlei Yu , Min Yu , Lihua Xu , Sumei Liu , Zewen Sun , Jianqiao Ye

This paper investigates the mechanical behavior of ultra-high-performance concrete-filled steel tubes (UHPCFST) under repeated eccentric compression. A total of 30 UHPCFST specimens are designed, fabricated, and tested. The design variables include steel tube thickness, UHPC type, loading eccentricity and load pattern. Failure modes, force-axial shortening curves, section strain distributions, lateral deflection distributions, bearing capacity and stiffness are studied. Three failure modes, i.e., steel tube bulge, compressive crush and tensile crack of the UHPC infill are observed. Specimens with larger loading eccentricity and thinner steel tube are more likely to exhibit all the three modes. Subjected to eccentric loading, the compressive strength and stiffness of the UHPCFST increase significantly with the increase of steel tube thickness and UHPC strength. In the case of repeated loading, stiffness degradation is observed. Existing formulas for the N-M curve and the eccentric compressive capacity are evaluated against the test results. A formula for eccentric compressive stiffness is derived based on the parabolic function assumption. Additionally, an empirical model is introduced to describe the force-axial shortening relationship of the UHPCFST under repeated eccentric compression, which may be applied in practical design and analysis.

本文研究了超高性能混凝土填充钢管（UHPCFST）在反复偏心压缩下的力学行为。共设计、制作和测试了 30 个 UHPCFST 试件。设计变量包括钢管厚度、UHPC 类型、加载偏心率和加载模式。对破坏模式、力-轴向缩短曲线、截面应变分布、侧向挠度分布、承载能力和刚度进行了研究。观察到三种破坏模式，即钢管隆起、压缩挤压和超高性能混凝土填充物的拉伸裂缝。加载偏心越大、钢管越薄的试样越有可能出现上述三种失效模式。在偏心加载条件下，随着钢管厚度和 UHPC 强度的增加，UHPCFST 的抗压强度和刚度也显著增加。在重复加载的情况下，会出现刚度下降。根据试验结果对现有的 N-M 曲线和偏心抗压能力公式进行了评估。根据抛物线函数假设推导出偏心压缩刚度公式。此外，还引入了一个经验模型来描述 UHPCFST 在反复偏心压缩下的力-轴向缩短关系，该模型可用于实际设计和分析。

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引用次数: 0

Machine learning for nano-level defect detection in aligned random carbon nanotubes-reinforced electrically conductive nanocomposite 机器学习用于对齐随机纳米碳管增强导电纳米复合材料中的纳米级缺陷检测

IF 6.3 2区材料科学 Q1 MATERIALS SCIENCE, COMPOSITES

Composite Structures

Pub Date : 2024-10-21 DOI: 10.1016/j.compstruct.2024.118651

Iskander S. Akmanov, Stepan V. Lomov, Mikhail Y. Spasennykh, Sergey G. Abaimov

Machine learning allows fast nano-scale defect detection in polymer-impregnated aligned carbon nanotube (CNT) nanocomposites. Digital twins were populated by TEM-validated geometry; considered defects were flat cracks and close-to-spherical voids. Finite-element analysis of piezoresistive response was conducted by embedment of CNT network into matrix. Identification of a defect by change in CNT network piezoresistivity was challenged by: (1) randomness of CNTs’ shapes and placement, ML training happened on random realisations; (2) high strength of CNTs leading to the preservation of conductive paths along CNTs and changes only in conductivities of tunnelling contacts. “Artificial approximation“ was introduced to economise computer time multi-fold: ML was trained on cases with artificially degraded tunnelling conductivities within the defect. Three ML models: XGBoost, fully connected, and convolution neural networks were employed. All models managed the task for near-spherical voids, but performed poorly for flat cracks, due to the limited number of tunnelling contacts in crack volume. When trained on the mixed set of voids and cracks, both neural networks demonstrated the ability to learn the difference and detected even cracks, while XGBoost was not up to the challenge. By metrics, the convolutional neural network demonstrated the highest accuracy of predictions.

通过机器学习可以快速检测聚合物浸渍对齐碳纳米管（CNT）纳米复合材料中的纳米级缺陷。通过 TEM 验证的几何形状填充了数字孪晶；考虑的缺陷为平面裂缝和近似球形的空隙。通过将 CNT 网络嵌入基体，对压阻响应进行了有限元分析。通过 CNT 网络压阻系数的变化来识别缺陷面临以下挑战：(1) CNT 的形状和位置具有随机性，ML 训练是在随机现实中进行的；(2) CNT 的高强度导致沿 CNT 的导电路径得以保留，仅隧道接触的电导率发生变化。引入了 "人工近似"，以成倍地节省计算机时间：在缺陷内隧道传导性人为降低的情况下进行 ML 训练。三种 ML 模型：采用了 XGBoost、全连接和卷积神经网络。对于近球形空洞，所有模型都能完成任务，但对于平面裂缝，由于裂缝体积中隧道接触的数量有限，因此表现不佳。当在空洞和裂缝混合集上进行训练时，两种神经网络都表现出了学习差异的能力，并能检测出均匀的裂缝，而 XGBoost 则无法应对挑战。从指标来看，卷积神经网络的预测准确率最高。

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引用次数: 0

The application of novel shear deformation theory and nonlocal elasticity theory to study the mechanical response of composite nanoplates 应用新型剪切变形理论和非局部弹性理论研究复合纳米板的力学响应

IF 6.3 2区材料科学 Q1 MATERIALS SCIENCE, COMPOSITES

Composite Structures

Pub Date : 2024-10-20 DOI: 10.1016/j.compstruct.2024.118646

Phan Quang Phuc , Pham Van Dong , Nguyen Trong Hai , Ashraf M. Zenkour , Luu Gia Thien

The use of composite structures, which have many layers of materials, has become more prevalent in the field of engineering. One of the advantages of this approach is its ability to use the inherent strengths of the constituent materials, resulting in a substantial increase in their load-bearing capability. Hence, this research represents the pioneering investigation into the static bending and free vibration characteristics of composite nanoplates including several layers of materials, whereby the material layers are interconnected via intricate profiles characterized by square wave and sine waveforms. The purpose of this endeavor is to fully capitalize on the benefits of attending courses in order to enhance practical working efficiency. This study also incorporates the use of two innovative third-order shear deformation theories. Simultaneously, considering the negligible size impact facilitated by the nonlocal theory, the mathematical formulations and equilibrium equations are derived using the Hamilton principle. The issue has been addressed using a four-node element with six degrees of freedom per node. One novel aspect of this study is its consideration of the impact of initial shape imperfections in various manifestations. Additionally, the elastic foundation incorporates characteristics that exhibit spatial variation. This statement provides a somewhat more accurate depiction of the behavior shown by actual structures. The numerical findings have been meticulously computed and thoroughly examined. Notably, it is possible to determine the optimal number of wavelengths in the profile to enhance the load-bearing capability of the structure. The findings derived from this study have significant value in informing the design of operational frameworks in practical settings.

工程领域越来越普遍地使用由多层材料组成的复合结构。这种方法的优点之一是能够利用组成材料的固有强度，从而大幅提高其承载能力。因此，本研究开创性地研究了包括多层材料在内的复合纳米板的静态弯曲和自由振动特性，这些材料层通过以方波和正弦波形为特征的复杂剖面相互连接。这项工作的目的是充分发挥参加课程的优势，以提高实际工作效率。本研究还采用了两种创新的三阶剪切变形理论。同时，考虑到非局部理论对尺寸的影响可以忽略不计，利用汉密尔顿原理推导出数学公式和平衡方程。该问题使用了每个节点具有六个自由度的四节点元素。这项研究的一个新颖之处是考虑了各种表现形式的初始形状缺陷的影响。此外，弹性地基还包含了空间变化特征。这在一定程度上更准确地描述了实际结构的行为。数值结果经过了精心计算和全面检查。值得注意的是，可以确定轮廓中的最佳波长数，以提高结构的承载能力。这项研究得出的结果对实际环境中操作框架的设计具有重要参考价值。

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引用次数: 0

Three-dimensional mesoscopic investigation on the dynamic compressive behavior of coral sand concrete with reinforced granite coarse aggregate (GCA) 对含强化花岗岩粗骨料（GCA）的珊瑚砂混凝土动态抗压行为的三维中观研究

IF 6.3 2区材料科学 Q1 MATERIALS SCIENCE, COMPOSITES

Composite Structures

Pub Date : 2024-10-19 DOI: 10.1016/j.compstruct.2024.118650

Ruiqi Guo , Jie Dong , Linjian Ma , Zhilin Long , Fu Xu , Changjun Yin

In the construction of island and reef engineering, coral concrete shows a good application prospect due to its abundant raw materials. However, the porous and fragile mechanical characteristics of coral reefs limit their use as coarse aggregate in the preparation of coral concrete materials. This study utilized hard and dense granite as the coarse aggregate and regarded coral sand concrete as a two-phase composite material consisting of spherical granite coarse aggregate (GCA) and coral mortar. It investigated the enhancement effect of granite on coral concrete from a microscopic perspective. Five 3D mesoscopic models with different GCA contents and randomly distributed aggregates were established to reveal the variation patterns and failure mechanisms of coral sand concrete under impact loading with GCA. The findings demonstrate that the K&C model can effectively simulate the dynamic compression behavior of coral mortar and granite materials. Under the action of a half-sine incident wave, the dynamic compressive strength of the samples increases with the increase in GCA, demonstrating that the addition of GCA can effectively enhance the impact resistance of coral sand concrete. As the content of GCA increases, the sensitivity of the samples to the loading wave amplitude also increases accordingly.

在岛屿和珊瑚礁工程建设中，珊瑚混凝土因其丰富的原材料而显示出良好的应用前景。然而，珊瑚礁多孔、脆弱的力学特性限制了其作为粗骨料用于珊瑚混凝土材料的制备。本研究利用坚硬致密的花岗岩作为粗骨料，将珊瑚砂混凝土视为由球形花岗岩粗骨料（GCA）和珊瑚砂浆组成的两相复合材料。它从微观角度研究了花岗岩对珊瑚混凝土的增强效果。研究建立了五个具有不同 GCA 含量和随机分布骨料的三维介观模型，以揭示珊瑚砂混凝土在 GCA 冲击荷载作用下的变化规律和破坏机理。研究结果表明，K&C 模型能有效模拟珊瑚砂浆和花岗岩材料的动态压缩行为。在半正弦入射波的作用下，样品的动态抗压强度随着 GCA 含量的增加而增加，表明添加 GCA 可以有效提高珊瑚砂混凝土的抗冲击性能。随着 GCA 含量的增加，样品对加载波幅的敏感性也相应增加。

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引用次数: 0

An efficient moving-mesh strategy for predicting crack propagation in unidirectional composites: Application to materials reinforced with aligned CNTs 预测单向复合材料裂纹扩展的高效移动网格策略：应用于使用排列有序的碳纳米管增强的材料

IF 6.3 2区材料科学 Q1 MATERIALS SCIENCE, COMPOSITES

Composite Structures

Pub Date : 2024-10-19 DOI: 10.1016/j.compstruct.2024.118652

Domenico Ammendolea , Francesco Fabbrocino , Lorenzo Leonetti , Paolo Lonetti , Arturo Pascuzzo

This paper presents an efficient numerical approach for reproducing the process of crack propagation inside unidirectional composites subjected to general loading conditions, with special reference to epoxy materials enhanced with embedded aligned CNTs. This approach involves a traditional FE framework improved by the Moving Mesh (MM) technique based on the Arbitrary Lagrangian-Eulerian (ALE) formulation and the Interaction Integral Method (M−integral). The MM serves as a powerful numerical tool to simulate the discrete crack advance with minimal remeshing, thus reducing the computational complexities. Instead, the M−Integral method, formulated for generally anisotropic materials, has been employed to extract the mixed-mode Stress Intensity Factors (SIFs), which are necessary to define the crack onset condition and propagation direction on the basis of the modified Maximum Hoop Stress Criterion. The proposed strategy includes the extended rule of mixtures to evaluate the homogenized elastic properties of nano-reinforced composites. The validity of the proposed methodology has been assessed through comparisons with experimental data and numerical results available in the literature.

本文介绍了一种有效的数值方法，用于再现单向复合材料在一般加载条件下的裂纹扩展过程，特别是嵌入排列的 CNT 增强环氧材料。该方法采用传统的有限元框架，通过基于任意拉格朗日-欧拉（ALE）公式和交互积分法（M-积分法）的移动网格（MM）技术加以改进。移动网格技术是一种强大的数值工具，可在最小重网格的情况下模拟离散裂纹的扩展，从而降低计算复杂度。而针对一般各向异性材料制定的 M-Integral 方法则用于提取混合模式应力强度因子（SIF），这是根据修正的最大箍筋应力准则定义裂纹起始条件和扩展方向所必需的。所提出的策略包括扩展的混合物规则，用于评估纳米增强复合材料的均质弹性特性。通过与文献中的实验数据和数值结果进行比较，对所提方法的有效性进行了评估。

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引用次数: 0

A homogenized constitutive model for 2D woven composites under finite deformation: Considering fiber reorientation 有限变形条件下二维编织复合材料的均质结构模型：考虑纤维重新定向

IF 6.3 2区材料科学 Q1 MATERIALS SCIENCE, COMPOSITES

Composite Structures

Pub Date : 2024-10-19 DOI: 10.1016/j.compstruct.2024.118649

Dake Wu , Zhangjie Yu , Xinfa Xiong , Ang Peng , Jian Deng , Deng’an Cai , Guangming Zhou , Xinwei Wang

Two-dimensional (2D) woven composites exhibit excellent mechanical properties along the fiber directions. The mechanical behaviors demonstrate nonlinearity in specific applications. Although plasticity methods can be applied to predict complex behaviors, however, fiber reorientation has been observed during finite deformation, indicating that the fiber directions are no longer along orthotropic material axes when the angle between fibers changes. The angular bisectors of two fiber directions can serve as the orthotropic material axes due to the rotational symmetries even in finite deformation scenarios. This study reports a homogenized nonlinear constitutive model based on the rotational symmetry axes, incorporating plasticity and fiber reorientation phenomena. The plasticity model contains a two-parameter flow potential and power function. Plastic deformations are computed using an explicit method. Fiber reorientation angles are computed both theoretically and numerically. The relationship between mechanical properties and fiber reorientation angles is studied using finite element method (FEM). Due to introduce of a novel approach to determining the strain and stress of 2D woven composites undergoing finite deformation, the proposed model should have potential in engineering predictions.

二维（2D）编织复合材料沿纤维方向具有优异的机械性能。在特定应用中，其机械性能表现出非线性。虽然塑性方法可用于预测复杂的行为，但在有限变形过程中已观察到纤维的重新定向，这表明当纤维之间的角度发生变化时，纤维方向不再沿着正交材料轴。由于旋转对称性，即使在有限变形情况下，两个纤维方向的角平分线也可以作为正交材料轴。本研究报告了一种基于旋转对称轴的均质化非线性结构模型，其中包含塑性和纤维重新定向现象。塑性模型包含一个双参数流动势能和幂函数。塑性变形采用显式方法计算。纤维重新定向角是通过理论和数值计算得出的。使用有限元法（FEM）研究了机械性能与纤维重新定向角之间的关系。由于引入了一种新方法来确定发生有限变形的二维编织复合材料的应变和应力，所提出的模型在工程预测中应具有潜力。

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引用次数: 0

Effect of Three-Dimensional auxetic honeycomb core on behavior of sound transmission loss in shallow sandwich cylindrical shell 三维辅助蜂窝芯对浅层夹层圆柱壳传声损耗行为的影响

IF 6.3 2区材料科学 Q1 MATERIALS SCIENCE, COMPOSITES

Composite Structures

Pub Date : 2024-10-16 DOI: 10.1016/j.compstruct.2024.118624

Mojtaba Sayad Ghanbari Nezhad , Mehrdad Motavasselolhagh , Roohollah Talebitooti , Fengxian XIN

The primary objective of this research is to examine the sound transmission loss (STL) in a shallow sandwich cylindrical shell featuring a 3D auxetic honeycomb core. Initially, the 3D elasticity theory was employed by applying the state vector method and extracting both local and global transfer matrices to calculate STL relations for the cylindrical shell, including the auxetic honeycomb core. Subsequently, boundary conditions were applied to calculate the unknowns, eventually leading to a relationship for calculating STL within the structure. The derived equations were numerically solved using MATLAB software. The validity of the results obtained using this method was examined by comparing them with the findings of other researchers. Moreover, a comparison was conducted involving a large ratio of the curvature radius to thickness, considering both the auxetic honeycomb core and aluminum with equal mass. The results demonstrate a significant increase in STL when utilizing this auxetic honeycomb core compared to a material with the same mass. Specifically, at a frequency of 2 Hz, a significant enhancement of about 29.44 % in STL is observed when increasing the core thickness from 10.39 mm to 20.39 mm. Furthermore, STL results have been obtained for various thicknesses, radius of curvature, and incident angles.

本研究的主要目的是研究具有三维辅助蜂窝芯的浅夹层圆柱形壳体的传声损耗（STL）。首先，采用三维弹性理论，应用状态矢量法，提取局部和全局传递矩阵，计算包括辅助蜂窝芯在内的圆柱形壳体的 STL 关系。随后，应用边界条件计算未知数，最终得出计算结构内 STL 的关系。推导出的方程使用 MATLAB 软件进行数值求解。通过与其他研究人员的研究结果进行比较，检验了使用这种方法得出的结果的有效性。此外，还对曲率半径与厚度之比较大的情况进行了比较，同时考虑到辅助蜂窝芯和铝的质量相等。结果表明，与相同质量的材料相比，使用这种辅助蜂窝芯时，STL 有明显增加。具体地说，在频率为 2 Hz 时，当内核厚度从 10.39 毫米增加到 20.39 毫米时，STL 显著增加了约 29.44%。此外，还获得了不同厚度、曲率半径和入射角的 STL 结果。

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引用次数: 0

A novel cellular structure with center-symmetric cell walls for morphing applications 用于变形应用的具有中心对称细胞壁的新型细胞结构

IF 6.3 2区材料科学 Q1 MATERIALS SCIENCE, COMPOSITES

Composite Structures

Pub Date : 2024-10-16 DOI: 10.1016/j.compstruct.2024.118644

Dezhi Wu, Guang Yang, Jianguo Tao, Yue Wang, Hong Xiao, Hongwei Guo

Cellular structures are potential candidates for the supporting framework of flexible morphing skins. Unlike traditional zero Poisson’s ratio (ZPR) cellular structures with axisymmetric cell walls, this paper proposes a novel cellular structure with center-symmetric cell walls. The in-plane mechanical properties of this novel structure are explored through theoretical analysis and substantiated by both finite element simulations and experimental tests. Compared to the classic accordion honeycomb structure, the elastic modulus in the x-direction of the novel structure is reduced by an average of 58%, the strain amplification rate is increased by 122%, and the in-plane stiffness anisotropy is improved by 200%. These findings suggest that the proposed structure offers far superior stiffness anisotropy and large deformation potential, making it more suitable for morphing applications than the traditional ZPR cellular structures.

细胞结构是柔性变形表皮支撑框架的潜在候选材料。与具有轴对称细胞壁的传统零泊松比（ZPR）细胞结构不同，本文提出了一种具有中心对称细胞壁的新型细胞结构。本文通过理论分析探讨了这种新型结构的平面力学性能，并通过有限元模拟和实验测试加以证实。与经典的风琴式蜂窝结构相比，新型结构 x 方向的弹性模量平均降低了 58%，应变放大率提高了 122%，面内刚度各向异性提高了 200%。这些研究结果表明，与传统的 ZPR 蜂窝结构相比，拟议的结构具有更优越的刚度各向异性和更大的变形潜力，更适合变形应用。

引用次数: 0

Damage evolution and failure mechanism of 2.5D woven composite tubes under quasi-static lateral compression 准静态横向压缩条件下 2.5D 编织复合管的损伤演变和破坏机理

IF 6.3 2区材料科学 Q1 MATERIALS SCIENCE, COMPOSITES

Composite Structures

Pub Date : 2024-10-11 DOI: 10.1016/j.compstruct.2024.118635

Yajuan Wang, Zunqing Wang, Xiaoxu Wang, Diantang Zhang

2.5D woven composites are ideal candidate materials for deep-sea pressure tubes owing to their excellent out-of-plane properties. This paper presents the damage evolution and failure mechanism of 2.5D woven composite tubes under quasi-static lateral compression. To conduct this study, 2.5D woven composite tubes with different thickness-to-diameter ratios, 0.04, 0.07 and 0.10, were designed and prepared. The quasi-static lateral compression tests were carried out in order to evaluate the progressive damage analysis, combining high speed photographic image with acoustic emission technologies. The results show that the increase of the ratio of thickness-to-diameter, the deformation and shear failure of the sample can be inhibited obviously. Due to the enhanced interlayer interaction, the lateral stiffness of the sample is obviously improved, so the lateral bearing stability of the sample is improved. When the peak load of samples with the thickness-to-diameter ratio of 0.1 reached 11.51 kN, it exceeded that of samples with thickness-to-diameter ratios of 0.04 and 0.07 by 450% and 82%, respectively. Furthermore, the failure mechanisms of samples with the thickness-to-diameter ratio of 0.1 were controlled by delamination fracture, whereas that of 0.04 and 0.07 were mainly influenced by shear failure and delamination failure, respectively.

2.5D 编织复合材料具有优异的平面外性能，是深海压力管的理想候选材料。本文介绍了 2.5D 编织复合材料管在准静态横向压缩下的损伤演变和失效机理。为了开展这项研究，设计并制备了不同厚度直径比（0.04、0.07 和 0.10）的 2.5D 编织复合管。为了评估渐进损伤分析，结合高速摄影图像和声发射技术，进行了准静态横向压缩试验。结果表明，随着厚径比的增加，样品的变形和剪切破坏得到明显抑制。由于层间相互作用增强，试样的横向刚度明显提高，因此试样的横向承载稳定性得到改善。当厚度与直径之比为 0.1 的试样的峰值载荷达到 11.51 kN 时，分别比厚度与直径之比为 0.04 和 0.07 的试样高出 450% 和 82%。此外，厚度与直径之比为 0.1 的样品的破坏机制主要由分层断裂控制，而厚度与直径之比为 0.04 和 0.07 的样品则分别主要受剪切破坏和分层破坏的影响。

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引用次数: 0

Vibration suppression characteristics of a thin sandwich panel with misaligned stacking spider-web-like phononic crystal cores 具有错位堆叠蛛网状声波晶体芯的薄夹芯板的振动抑制特性

IF 6.3 2区材料科学 Q1 MATERIALS SCIENCE, COMPOSITES

Composite Structures

Pub Date : 2024-10-11 DOI: 10.1016/j.compstruct.2024.118642

Fulong Zhao, Tongtong Huo, Zhijing Wu, Fengming Li

A novel spider-web-like multi-hole variable cross-section phononic crystal (VCSPC) is proposed in this study, along with a misaligned stacking approach for constructing thin sandwich panels to achieve lightweight and compact structures for low-frequency vibration suppression. The band-gap (BG) characteristics and vibration modes are analyzed using the finite element method (FEM). To validate the effectiveness of the misaligned stacking approach, the finite element simulation and experimental verification of the frequency response function (FRF) are conducted. The results demonstrate that the spider-web-like configuration, with distributed masses and periodically varying cross-sections, can reduce the opening frequencies of BGs. When compared to the conventional linearly arranged panel, the misaligned stacking structure exhibits equivalent vibration BGs and attenuation characteristics. It is important to note that the misaligned stacking design significantly reduces the size in the direction of vibration attenuation. This type of thin sandwich panel is well-suited for engineering environments with size limitations on vibration reduction structures. The proposed strategy facilitates the use of large-scale phononic crystals for low-frequency vibration control, thereby promoting the application of phononic crystals in engineering through a more compact structural design.

本研究提出了一种新颖的蛛网状多孔变截面声子晶体（VCSPC），并采用错位堆叠法构建薄夹层板，以实现轻质、紧凑的低频振动抑制结构。研究采用有限元法（FEM）分析了带隙（BG）特性和振动模式。为了验证错位堆叠方法的有效性，对频率响应函数（FRF）进行了有限元模拟和实验验证。结果表明，具有分布式质量和周期性变化横截面的蛛网状构造可以降低 BG 的开口频率。与传统的线性排列面板相比，错位堆叠结构表现出同等的振动 BG 和衰减特性。值得注意的是，错位堆叠设计大大减小了振动衰减方向上的尺寸。这种薄型夹层板非常适合对减振结构尺寸有限制的工程环境。所提出的策略有助于利用大规模声子晶体进行低频振动控制，从而通过更紧凑的结构设计促进声子晶体在工程中的应用。

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引用次数: 0