On the Magnetically Tunable Free Damped-Vibration of L-Shaped Composite Spherical Panels Made of GPL-Reinforced Magnetorheological Elastomers: An Element-Based GDQ Approach

IF 6.6 1区工程技术 Q1 ENGINEERING, CIVIL

Thin-Walled Structures Pub Date : 2025-09-13 DOI:10.1016/j.tws.2025.113987

Peijun Zhang , Zhen Wang , Huaigu Tian , Xiaojian Xi , Xiaogang Liu

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引用次数: 0

Abstract

In practical engineering applications, curved structures rarely conform to idealized rectangular or circular planforms and often involve far more intricate geometries. Among these, L-shaped spherical panels have emerged as a structurally significant form, found in subsystem interfaces, aerospace fuselage junctions, complex biomedical shells, and multifunctional architectural surfaces. This study explores the free damped-vibration behavior of such panels constructed from a graphene platelet (GPL)-reinforced magnetorheological elastomer (MRE) nanocomposite. Unlike conventional elastic matrices, the MRE base material exhibits time- and field-dependent viscoelastic behavior, influenced by both magnetic field intensity and ferromagnetic content. This behavior is mathematically formulated through an experimentally validated generalized Kelvin–Voigt-type model, tailored to represent the storage and dissipation characteristics of the matrix under dynamic excitation. The reinforcing particles are graded through the panel thickness. The effective elastic properties of the composite are homogenized using the Halpin–Tsai micromechanical model, accounting for the influence of GPL content and sizes. To address the geometric complexity, a hybrid element-based GDQ (generalized differential quadrature) approach is developed. The L-shaped spherical panel is subdivided into rectangular elements, each governed by equations derived using Hamilton’s principle, first-order shear deformation theory, and Sander’s strain-displacement relations. Discretization via quadrature nodes enables the GDQ method to transform the governing PDEs into an efficient algebraic system. The global system is constructed by enforcing both displacement and force continuity at shared nodes and applying appropriate boundary conditions. The proposed framework achieves excellent accuracy in capturing frequencies and loss factors, demonstrating its capability for efficient dynamic analysis of non-standard. In addition to validating the accuracy of the proposed approach against benchmark problems, the study reveals distinct mode-switching and mode-jumping phenomena triggered by changes in geometric parameters—highlighting the sensitivity of vibrational behavior to panel shape and reinforcing the need for precise modeling in advanced smart structures.

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gpl增强磁流变弹性体l型复合球面板的磁可调自由阻尼振动：基于单元的GDQ方法

在实际工程应用中，弯曲结构很少符合理想的矩形或圆形平面，而且往往涉及更复杂的几何形状。其中，l形球形板已成为一种结构上重要的形式，用于子系统接口、航空航天机身连接处、复杂的生物医学外壳和多功能建筑表面。本研究探讨了由石墨烯血小板（GPL）增强磁流变弹性体（MRE）纳米复合材料构建的这种面板的自由阻尼振动行为。与传统的弹性基体不同，MRE基材料表现出与时间和场相关的粘弹性行为，受磁场强度和铁磁含量的影响。这种行为是通过实验验证的广义kelvin - voigt型模型在数学上表述的，该模型专门用于表示矩阵在动态激励下的存储和耗散特性。增强颗粒按面板厚度分级。考虑GPL含量和尺寸的影响，采用Halpin-Tsai微观力学模型对复合材料的有效弹性性能进行均匀化。为了解决几何复杂性，提出了一种基于混合单元的广义微分求积方法。l形球形面板被细分为矩形单元，每个单元由Hamilton原理、一阶剪切变形理论和Sander应变-位移关系导出的方程控制。通过正交节点的离散化使GDQ方法能够将控制偏微分方程转化为有效的代数系统。全局系统是通过在共享节点上强制位移和力的连续性并应用适当的边界条件来构建的。该框架在捕获频率和损耗因子方面具有很高的精度，证明了其对非标动态分析的有效性。除了针对基准问题验证所提出方法的准确性外，该研究还揭示了几何参数变化引发的不同模式切换和模式跳跃现象，突出了面板形状对振动行为的敏感性，并加强了对高级智能结构精确建模的需求。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Thin-Walled Structures 工程技术-工程：土木

CiteScore

9.60

自引率

20.30%

发文量

801

审稿时长

66 days

期刊介绍： Thin-walled structures comprises an important and growing proportion of engineering construction with areas of application becoming increasingly diverse, ranging from aircraft, bridges, ships and oil rigs to storage vessels, industrial buildings and warehouses. Many factors, including cost and weight economy, new materials and processes and the growth of powerful methods of analysis have contributed to this growth, and led to the need for a journal which concentrates specifically on structures in which problems arise due to the thinness of the walls. This field includes cold– formed sections, plate and shell structures, reinforced plastics structures and aluminium structures, and is of importance in many branches of engineering. The primary criterion for consideration of papers in Thin–Walled Structures is that they must be concerned with thin–walled structures or the basic problems inherent in thin–walled structures. Provided this criterion is satisfied no restriction is placed on the type of construction, material or field of application. Papers on theory, experiment, design, etc., are published and it is expected that many papers will contain aspects of all three.