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Investigation of the Impact of Thermo-Stamping, Fiber Orientation, and Metal Thickness on the Formability of Fiber Metal Laminates 研究热冲压、纤维方向和金属厚度对纤维金属层压板成型性的影响
IF 2.3 4区 材料科学 Q3 MATERIALS SCIENCE, COMPOSITES Pub Date : 2024-07-10 DOI: 10.1007/s10443-024-10250-z
Hamza Blala, Cheng Pengzhi, Zhang Shenglun, Cheng Gang, Ruan Shangwen, Meng Zhang

Despite being invented several decades ago, fiber metal laminates (FMLs) still encounter challenges in large-scale manufacturing, especially in forming small and complex-shaped components. These challenges arise from the limited strain rate of the fiber layers compared to the metallic layers. Consequently, conventional approaches to form FML parts are often inadequate. To produce parts free of defects such as fractures and wrinkles, this study investigates the effects of Thermo-stamping (TH-S), in addition to fiber orientation, on the forming behavior of FMLs, employing two different aluminum layer thicknesses. A comprehensive approach combining finite element simulations and experimental analyses was employed. The study investigated thinning of aluminum alloy layers, stress distributions across different layers, and the influence of fiber orientation. The FML blanks are made of a middle woven glass fiber prepreg with a thickness of 0.2 mm, using a thermosetting epoxy system, and Al 2024-T3 alloy sheets with varying thicknesses of 0.3 mm and 0.5 mm. Material behavior was evaluated using Abaqus software, applying the Johnson-Cook criterion for damage initiation in ductile metals and Hashin’s theory for damage initiation in fiber-reinforced composites. These simulations were then compared with experimental results. The findings highlight the potential of the TH-S process to enhance the forming performance of FMLs, particularly evident in the case of the 0°/45° middle layer fiber, which exhibits a higher forming depth and a more uniform thickness distribution. Additionally, a greater flexibility of the glass fiber under the 0°/45° layup compared to the 0/90 layup was detected. This flexibility provides the aluminum layers with more freedom of deformation in the plastic domain. These advancements hold promise for widespread industrial applications of FMLs.

尽管纤维金属层压板(FMLs)早在几十年前就已发明,但在大规模制造过程中,尤其是在制造形状复杂的小型部件时,仍会遇到各种挑战。这些挑战源于纤维层与金属层相比有限的应变率。因此,传统的 FML 零件成型方法往往是不够的。为了生产出无断裂和褶皱等缺陷的零件,本研究采用两种不同厚度的铝层,研究了热冲压(TH-S)以及纤维取向对 FML 成型行为的影响。研究采用了一种结合有限元模拟和实验分析的综合方法。研究调查了铝合金层的减薄、不同层间的应力分布以及纤维取向的影响。FML 坯料由厚度为 0.2 毫米的中间编织玻璃纤维预浸料和厚度为 0.3 毫米和 0.5 毫米的铝 2024-T3 合金板材组成,预浸料采用热固性环氧树脂体系。使用 Abaqus 软件对材料行为进行了评估,应用约翰逊-库克准则评估了韧性金属的损伤起始,并应用哈申理论评估了纤维增强复合材料的损伤起始。然后将这些模拟结果与实验结果进行了比较。研究结果凸显了 TH-S 工艺在提高 FML 成型性能方面的潜力,尤其是在 0°/45° 中间层纤维的情况下,其成型深度更高,厚度分布更均匀。此外,与 0/90 层压相比,0°/45° 层压下的玻璃纤维具有更大的柔韧性。这种柔韧性为铝层提供了更大的塑性变形自由度。这些进步为 FML 的广泛工业应用带来了希望。
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引用次数: 0
Development of a Flexible Porous GNP-PDMS Composite: Tunable Thermal and Electrical Properties for Novel Applications 开发柔性多孔 GNP-PDMS 复合材料:用于新型应用的可调热学和电学特性
IF 2.3 4区 材料科学 Q3 MATERIALS SCIENCE, COMPOSITES Pub Date : 2024-07-09 DOI: 10.1007/s10443-024-10246-9
Mohamad-Anas Hejazi, Levent Trabzon

The integration of carbon nanomaterials with flexible polymers has received intensive attention as a promising research direction in developing materials with novel properties for advanced applications. Herein, we report on the fabrication and characterization of flexible porous polydimethylsiloxane (PDMS) coated with graphene nanoplatelets (GNPs). We explore the mechanisms affecting its various properties under deformation, and propose new applications for it. The results show lightweight and excellent flexibility characteristics for the obtained GNP-PDMS composite. Measurements of its electrical resistance revealed a change in the electrical resistivity from 2.35 × 106 Ω·m to 194 Ω·m under a strain change from 10 to 80% illustrating its ability to shift behavior from an electrical insulator to a relatively low resistivity material and demonstrating the considerable potential for use as a flexible electrical switch. Moreover, the thermal conductivity of GNP-PDMS was found to be significantly enhanced (up to ∼ 110%) by changing the level of compression from 20 to 80%, proving a strain-tunable thermal performance, allowing its utilization as an insulation material of variable conductance for unique thermal management applications.

碳纳米材料与柔性聚合物的结合作为开发具有新颖特性的先进应用材料的一个有前途的研究方向受到了广泛关注。在此,我们报告了涂有石墨烯纳米片(GNPs)的柔性多孔聚二甲基硅氧烷(PDMS)的制备和表征。我们探讨了影响其变形时各种性能的机理,并提出了新的应用建议。研究结果表明,所获得的 GNP-PDMS 复合材料具有轻质、柔韧的特点。对其电阻的测量显示,在应变从 10% 到 80% 的变化过程中,电阻率从 2.35 × 106 Ω-m 变为 194 Ω-m,这说明它能够从电绝缘材料转变为电阻率相对较低的材料,并证明了其作为柔性电子开关的巨大应用潜力。此外,通过将压缩程度从 20% 变为 80%,GNP-PDMS 的热导率显著提高(高达 ∼ 110%),证明了其具有应变可调的热性能,可用作具有可变电导率的绝缘材料,用于独特的热管理应用。
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引用次数: 0
Optimal Design Study of Vibro-Acoustic Resistance of Porous Foam Composite Laminates 多孔泡沫复合层压板抗振声性能的优化设计研究
IF 2.3 4区 材料科学 Q3 MATERIALS SCIENCE, COMPOSITES Pub Date : 2024-07-04 DOI: 10.1007/s10443-024-10241-0
Haiyang Zhang, Zelin Li, Yichen Deng, Hui Li, Hang Cao, Xiangping Wang

Optimal design study of vibro-acoustic resistance of porous foam composite laminates (PFCLs) is presented in this paper. A dynamic model of the PFCLs subjected to the plane acoustic excitation load is firstly proposed with consideration of upper and lower composite skins and a uniform porous foam. The vibration and acoustic solutions of the PFCLs with acoustic energy excitation are further acquired using the first-order shear deformation theory, the finite element method, the Rayleigh integral approach, the mode superposition technique, etc. Subsequently, a vibro-acoustic optimization model is established by accounting for appropriate design variables and constraints, in which resonance responses, sound transmission losses, and overall structural mass are taken as objective functions, respectively, and the artificial immune clonal selection algorithm is adopted to improve the efficiency in the optimization calculations. After such an algorithm and the current model are thoroughly validated, single-objective, dual-objective, and multi-objective optimizations are undertaken on the PFCLs to achieve the optimal design parameters. The research results indicate that it is hard to enhance the vibro-acoustic resistance and lightweight property of the PFCLs simultaneously, which means some compromise results of design parameters need to be chosen. It is suggested to determine the concerned optimal design results by referring to the nearby turning points associated with the Pareto-optimal solutions.

本文对多孔泡沫复合材料层压板(PFCL)的抗振声性能进行了优化设计研究。首先提出了 PFCL 在平面声激励载荷作用下的动态模型,并考虑了上下复合材料表皮和均匀的多孔泡沫。利用一阶剪切变形理论、有限元法、瑞利积分法、模态叠加技术等,进一步获得了声能激励下 PFCL 的振动和声学解。随后,通过考虑适当的设计变量和约束条件,建立了振动声学优化模型,分别将共振响应、传声损失和整体结构质量作为目标函数,并采用人工免疫克隆选择算法来提高优化计算的效率。在对该算法和当前模型进行充分验证后,对 PFCL 进行了单目标、双目标和多目标优化,以实现最优设计参数。研究结果表明,很难同时提高 PFCL 的抗振性和轻质特性,这意味着需要选择一些折中的设计参数。建议参考与帕累托最优解相关的临近转折点来确定相关的最优设计结果。
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引用次数: 0
Review on Mechanical Performance of Fibre-Reinforced Plastics in Marine Environments 纤维增强塑料在海洋环境中的机械性能综述
IF 2.3 4区 材料科学 Q3 MATERIALS SCIENCE, COMPOSITES Pub Date : 2024-07-04 DOI: 10.1007/s10443-024-10247-8
Norman Osa-uwagboe, Vadim V. Silberschmidt, Emrah Demirci

Fibre-reinforced plastics (FRPs) are increasingly popular in marine applications, such as boats, offshore wind-power installations, as well as oil and gas offshore systems thanks to their high stiffness, light weight, and damage resistance. This paper aims to examine the recent developments in the investigation of the effects of moisture uptake on the mechanical performance of FRP for maritime applications, to identify the gaps in the literature, and to suggest likely future research directions in this area. While the review is limited to recent studies—within the last two decades, it discusses in detail the current advances in the experimental investigations of moisture uptake on critical mechanical performance including tensile, flexural, shear and viscoelastic properties, thus covering the major quasi-static and dynamic regimes of FRPs subjected to seawater exposure.

纤维增强塑料(FRP)具有刚度高、重量轻和抗破坏性强等优点,在船舶、海上风力发电装置以及石油和天然气海上系统等海洋应用中越来越受欢迎。本文旨在研究在海洋应用中吸湿对玻璃钢机械性能影响的最新进展,找出文献中的不足,并提出该领域未来可能的研究方向。虽然综述仅限于过去二十年内的最新研究,但它详细讨论了吸湿对关键机械性能(包括拉伸、弯曲、剪切和粘弹性能)影响的实验研究的最新进展,从而涵盖了玻璃钢暴露于海水中的主要准静态和动态状态。
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引用次数: 0
A Machine Learning Boosted Data Reduction Methodology for Translaminar Fracture of Structural Composites 针对结构复合材料横向断裂的机器学习增强数据缩减方法
IF 2.3 4区 材料科学 Q3 MATERIALS SCIENCE, COMPOSITES Pub Date : 2024-07-01 DOI: 10.1007/s10443-024-10236-x
Davide Mocerino, Moisés Zarzoso, Federico Sket, Jon Molina, Carlos González

This work explored a machine learning (ML) algorithm as a fast data reduction method for translaminar fracture energy in composite laminates. The method was validated with translaminar fracture tests on compact tension (CT) specimens on AS4/8552 and IM7/8552 cross-ply lay-ups. Experimental fracture energy and R-curves for both materials were determined using the most common data reduction methods, such as the compliance calibration (CC), the area (AM) and the Irwin relationship (IM). Our new data reduction method uses a surrogate model based on an artificial neural network (ANN) trained with synthetic data generated with the cohesive crack finite element model. Such a surrogate model maps the cohesive properties with the corresponding load–displacement, crack-displacement and energy-displacement curves with interrogation times in the order of 20 ms and relative errors in the load–displacement and crack growth less than 2%. Such performance enabled its encapsulation to approximate the inverse problem to infer the cohesive parameters with the maximum likelihood estimator (MLE) directly from the experimental load–displacement and crack-displacement curves. The results demonstrated the ability of the model to deliver cohesive parameter inference directly from the macroscopic tests carried out at the laboratory level.

这项研究探索了一种机器学习(ML)算法,作为复合材料层压板层间断裂能的快速数据缩减方法。该方法通过对 AS4/8552 和 IM7/8552 交叉层压材料的紧凑拉伸 (CT) 试样进行层间断裂测试进行了验证。这两种材料的实验断裂能和 R 曲线都是使用最常见的数据还原方法确定的,如顺应性校准 (CC)、面积 (AM) 和欧文关系 (IM)。我们的新数据还原方法使用的是基于人工神经网络(ANN)的代用模型,该人工神经网络由内聚裂纹有限元模型生成的合成数据训练而成。这种代用模型将内聚特性与相应的载荷-位移、裂纹-位移和能量-位移曲线进行映射,询问时间约为 20 毫秒,载荷-位移和裂纹增长的相对误差小于 2%。这样的性能使其能够封装成近似逆问题,直接从实验载荷-位移和裂缝-位移曲线用最大似然估计法(MLE)推断内聚参数。结果表明,该模型能够直接从实验室进行的宏观测试中推断内聚参数。
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引用次数: 0
Response Surface Model for Mechanical Properties of Robotically Stitched Composites 机器人缝合复合材料机械性能的响应面模型
IF 2.3 4区 材料科学 Q3 MATERIALS SCIENCE, COMPOSITES Pub Date : 2024-06-27 DOI: 10.1007/s10443-024-10245-w
Radwa Alaziz, Shuvam Saha, Rani W. Sullivan

Composite structures are extensively used in several industries such as aerospace, automotive, sports, and construction due to their many advantages, including tailorable mechanical properties, high strength-to-weight ratios, and high specific stiffness. However, due to their low interlaminar tensile and shear strength, composites are prone to delaminations, which can degrade the overall mechanical performance of the structure. Through-thickness stitching provides a third-direction reinforcement to enhance the interlaminar tensile and shear strengths. In this study, quasi-isotropic composite test specimens were manufactured with a novel through-thickness robotic chain stitching with different patterns and tested under uniaxial tensile and three-point bend loadings. A design of experiments (DoE) approach was used to investigate the influence of stitch parameters (stitch density, stitch angle, and linear thread density) on the tensile strength, tensile modulus, and flexural strength of stitched composites. Experimental results are then used to develop a statistically informed response surface model (RSM) to find optimal stitching parameters based on a maximum predicted tensile strength, tensile modulus, and flexural strength. This study reveals and discusses the optimum selection of stitch processing parameters to improve the in-plane and out-of-plane mechanical properties.

复合材料结构具有多种优点,包括可定制的机械性能、高强度重量比和高比刚度,因此被广泛应用于航空航天、汽车、运动和建筑等多个行业。然而,由于层间拉伸和剪切强度较低,复合材料容易发生分层,从而降低结构的整体机械性能。通厚缝合可提供第三方向的加固,从而提高层间拉伸和剪切强度。在本研究中,使用新型通厚机器人链式缝合技术制作了不同模式的准各向同性复合材料试样,并在单轴拉伸和三点弯曲载荷下进行了测试。实验设计(DoE)方法用于研究缝合参数(缝合密度、缝合角度和线性线密度)对缝合复合材料拉伸强度、拉伸模量和弯曲强度的影响。然后利用实验结果建立了一个统计响应面模型(RSM),根据最大预测拉伸强度、拉伸模量和弯曲强度找到最佳缝合参数。这项研究揭示并讨论了缝合加工参数的最佳选择,以改善面内和面外机械性能。
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引用次数: 0
Nanoplatelet Orientation and Young’s Modulus of Graphene/Phenoxy Nanocomposites 石墨烯/苯氧基纳米复合材料的纳米小板取向和杨氏模量
IF 2.3 4区 材料科学 Q3 MATERIALS SCIENCE, COMPOSITES Pub Date : 2024-06-19 DOI: 10.1007/s10443-024-10243-y
Han Lin, Prasad Potluri, William W. Sampson, Arthur N. Wilkinson

We report on the development of phenoxy-graphene nano-composite fibres for improving the toughness of thermoset composites. In this paper, a systematic experimental investigation into the underlying mechanisms of graphene nanoplatelets (GNP) reinforcement of phenoxy nanocomposite fibres prepared via melt spinning is provided. The analysis reveals a tangential orientation of GNP in the outer layer of the fibres, while such orientation is absent in the fibre core region. We show that the relative size of the fibre sheath depends on process variables and exhibits a linear relationship with the modulus of GNP obtained via theoretical analysis using simple rule of mixtures. This is because the area ratio (AR) is proportional to the orientation degree of GNP. This indicates that the enhancement of the Young’s modulus of fibres mainly originates from the increased AR of the fibre sheath layer where the orientation of GNP is more regular.

我们报告了用于改善热固性复合材料韧性的苯氧基-石墨烯纳米复合纤维的开发情况。本文对通过熔融纺丝法制备的苯氧基纳米复合纤维的石墨烯纳米片(GNP)增强机理进行了系统的实验研究。分析表明,GNP 在纤维外层呈切向取向,而在纤维核心区域则没有这种取向。我们的研究表明,纤维鞘的相对尺寸取决于工艺变量,并与通过使用简单混合物规则进行理论分析获得的 GNP 模量呈线性关系。这是因为面积比 (AR) 与 GNP 的取向度成正比。这表明,纤维杨氏模量的提高主要源于 GNP 取向更规则的纤维鞘层 AR 的增加。
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引用次数: 0
Large-Deformation Electrothermal Actuation Inchworm-Like Crawling Robot Based on Bistable Structures for Load Carrying 基于双稳态结构的大变形电热致动寸虫式爬行机器人,用于承载负荷
IF 2.3 4区 材料科学 Q3 MATERIALS SCIENCE, COMPOSITES Pub Date : 2024-06-14 DOI: 10.1007/s10443-024-10242-z
Zheng Zhang, Tianye Wang, Tao Zhang, Hongcheng Shen, Baisong Pan, Min Sun, Guang Zhang, Shaofei Jiang

Crawling robots have great potential in some harsh environments, but there are still some limitations, such as tiny structures that can only produce small deformation and poor load-carrying capacity. A lightweight inchworm-like crawling robot made of bistable structure driven by electrothermal actuation is proposed in this paper. The robot has the characteristics of large deformation and a certain extent of load capacity. The motion of the crawling robot was realized by the common effect of the bistable structure and the designed feet with anisotropic friction. The unstable transition process between snap-through and snap-back processes of the bistable structure was utilized to provide morphological deformation. Meanwhile the feet with anisotropic friction transformed the deformation to unidirectional movement of the crawling robot. Through electric experiments, the electrothermal driving influencing factors of bistable structure are tested, including heating time, maximum temperature and curvature change, which demonstrates the possibility of driving inchworm-like crawling robot with bistable structure and large-deformation. And the structure of the inchworm-like crawling robot assembled by a bistable shell pasted with an electric heating sheet and the designed feet with anisotropic friction. In order to evaluate the motion properties and load-carrying function of the inchworm-like crawling robot, the step length test under different voltages and the experiment of the crawling robot load-carrying capacity were completed. The results show that the crawling robot performs well in load-carrying, can achieve crawling movement under the condition of carrying 10 g and 20 g objects. The inchworm-like crawling robot provides a method to achieve large-deformation and load-carrying and demonstrates it is suitable in some extreme environments.

爬行机器人在一些恶劣环境中具有巨大潜力,但仍存在一些局限性,如结构微小,只能产生很小的变形,承载能力差等。本文提出了一种由电热驱动双稳态结构制成的轻型尺蠖状爬行机器人。该机器人具有大变形和一定承载能力的特点。爬行机器人的运动是在双稳态结构和设计的各向异性摩擦脚的共同作用下实现的。利用双稳态结构在 "卡穿 "和 "卡回 "之间的不稳定过渡过程来实现形态变形。同时,各向异性摩擦脚将变形转化为爬行机器人的单向运动。通过电学实验,测试了双稳态结构的电热驱动影响因素,包括加热时间、最高温度和曲率变化,证明了双稳态结构和大变形驱动类尺蠖爬行机器人的可能性。在双稳态外壳上粘贴电加热片,并设计出具有各向异性摩擦力的脚,从而组装出了类尺蠖爬行机器人的结构。为了评估类尺蠖爬行机器人的运动特性和承载功能,完成了不同电压下的步长测试和爬行机器人承载能力实验。结果表明,爬行机器人的承载性能良好,能在承载10 g和20 g物体的条件下实现爬行运动。类似尺蠖的爬行机器人提供了一种实现大变形和承载的方法,并证明它适用于一些极端环境。
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引用次数: 0
Experimental Investigation and Numerical Simulation of Bonded, Bolted, and Hybrid Joints in CFRP Laminates Under Tensile Loading 拉伸载荷下 CFRP 层压材料中粘接、螺栓连接和混合连接的实验研究与数值模拟
IF 2.3 4区 材料科学 Q3 MATERIALS SCIENCE, COMPOSITES Pub Date : 2024-06-03 DOI: 10.1007/s10443-024-10240-1
Yiming Shangguan, Wenjing Wang, Anrui He, Junsheng Qu

In this study, an in-depth analysis is carried out to simulate the failure mechanism of T700 carbon fiber-reinforced polymer composite (CFRP) joints with a layup sequence of [45/-45/0/90]3 s when subjected to tensile loading, both experimentally and numerically. We compared the mechanical performance of three different edge-to-bolt diameter ratios (E/d) of bonded, bolted, and hybrid single lap joints subjected to tensile loading. A finite element-based progressive damage method (PDM) along with the bilinear triangular cohesive zone model (BTCZM) is developed to predict the damage evolution and failure mechanism for all joint configurations. By juxtaposing the simulation outcomes and the experimental data, we observed the failure morphology and assessed the bearing capacity of the joint under tensile loading. The comparison results revealed a minor discrepancy of merely 5.5% in terms of joint load capacity between simulations and experiments, which indicates the high accuracy of our model. The strength of the adhesive and mechanical joints increases with E/d from 3 to 5; however, the strength of the hybrid joints decreases. At E/d = 3, hybrid joints performed significantly better than bonded ones, with a remarkable enhancement of 41.53%. However, for E/d ratios of 4 and 5, both simulation results and test data showed that hybrid joints were inferior to bolted joints. The analytical methodology presented in this paper offers a valuable reference for future analysis and design of composite joints.

本研究通过实验和数值模拟,深入分析了铺层顺序为 [45/-45/0/90]3 s 的 T700 碳纤维增强聚合物复合材料(CFRP)接头在承受拉伸荷载时的失效机理。我们比较了三种不同边缘与螺栓直径比(E/d)的粘接接头、螺栓接头和混合单搭接接头在承受拉伸荷载时的机械性能。我们开发了基于有限元的渐进损伤法(PDM)和双线性三角内聚区模型(BTCZM),以预测所有接头结构的损伤演变和失效机制。通过将模拟结果与实验数据并列,我们观察了破坏形态,并评估了拉伸荷载下接头的承载能力。对比结果显示,模拟结果与实验结果在接头承载能力方面的差异很小,仅为 5.5%,这表明我们的模型具有很高的准确性。在 E/d 值为 3 到 5 的范围内,粘合剂接头和机械接头的强度随 E/d 值的增加而增加,但混合接头的强度却有所降低。当 E/d = 3 时,混合接头的性能明显优于粘接接头,显著提高了 41.53%。然而,当 E/d 比率为 4 和 5 时,模拟结果和测试数据都表明混合接头的性能不如螺栓接头。本文介绍的分析方法为今后分析和设计复合材料接头提供了宝贵的参考。
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引用次数: 0
Free and Forced Vibration Analysis of Carbon/Glass Hybrid Composite Laminated Plates Under Arbitrary Boundary Conditions 任意边界条件下碳/玻璃混合复合材料层压板的自由和强迫振动分析
IF 2.3 4区 材料科学 Q3 MATERIALS SCIENCE, COMPOSITES Pub Date : 2024-06-03 DOI: 10.1007/s10443-024-10235-y
Mengzhen Li, Carlos Guedes Soares, Zhiping Liu, Peng Zhang

This paper presents the theoretical investigations on the free and forced vibration behaviours of carbon/glass hybrid composite laminated plates with arbitrary boundary conditions. The unknown allowable displacement functions of the physical middle surface are expressed in terms of standard cosine Fourier series and sinusoidal auxiliary functions to ensure the continuity of the displacement functions and their derivatives at the structural boundaries. Arbitrary boundary conditions are achieved through the introduction of an artificial spring technique. The first shear deformation theory and Lagrange equations are utilized to derive the energy expression, and the eigenvalue equations associated with free and forced vibration are obtained by Rayleigh-Ritz variational operations. Subsequently, these equations are then solved to determine the natural frequency, mode of vibration, and the steady-state displacement response under forced excitation. The new results are compared with those from references and finite element methods to verify the convergence, accuracy and efficiency of the analytical method. The effects of hybrid ratios, stacking sequences, lamination schemes, fibre orientation, boundary conditions and excitation force on the free and forced vibration behaviours of the carbon/glass hybrid composite laminated plates are analyzed in detail.

本文对任意边界条件下碳/玻璃混合复合材料层压板的自由振动和强迫振动行为进行了理论研究。物理中间表面的未知允许位移函数用标准余弦傅里叶级数和正弦辅助函数表示,以确保位移函数及其导数在结构边界处的连续性。通过引入人工弹簧技术实现了任意边界条件。利用第一剪切变形理论和拉格朗日方程推导出能量表达式,并通过雷利-里兹变分运算获得与自由振动和受迫振动相关的特征值方程。随后,对这些方程进行求解,以确定受迫振动下的固有频率、振动模式和稳态位移响应。新结果与参考文献和有限元方法的结果进行了比较,以验证分析方法的收敛性、准确性和效率。详细分析了混合比、堆叠顺序、层压方案、纤维取向、边界条件和激振力对碳/玻璃混合复合材料层压板自由振动和强迫振动行为的影响。
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引用次数: 0
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Applied Composite Materials
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