带元表面的圆板的挠性边缘波和可定制的局部模式

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling Pub Date : 2024-10-12 DOI:10.1016/j.apm.2024.115749

Yizhou Shen , Pengfei Jiang , Feng Liu , Yanlong Xu , Zhichun Yang

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引用次数: 0

摘要

在这项研究中，我们研究了圆板挠曲边缘波（又称圆边波）的传播，提出了操纵这些波的元表面设计策略，并在边缘波操纵的基础上实现了可定制的边缘模式。本文提出了理论框架，以求解沿不同边界传播的圆边波的频散关系，这些边界包括自由边、具有微弱刚度的条带和具有槽阵列的元表面。在这些框架的基础上，揭示了圆边波的传播特性，并通过构造元表面实现了彩虹反射和拓扑界面状态。此外，还探讨了模态频率预测、对结构参数的鲁棒性以及圆边模态的有效激励位置。最后，在上述分析的基础上，提出了可定制的局部模态，这意味着可以在不改变相应模态频率的情况下设计模态形状中高能量区域的位置。我们的工作为操纵圆板中的挠曲波提供了一个新思路，并发现了挠曲波与振动之间的潜在关联，这可能会在振动控制和声学设备开发中得到广泛应用。

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Flexural edge waves and customizable local modes of circular plates with metasurface

In this research, we study the propagation of flexural edge waves of circular plates (also known as circular-edge waves), present design strategies of metasurfaces for manipulating these waves, and realize customizable edge modes on the basis of edge wave manipulations. Theoretical frameworks are presented to solve the dispersion relationship of circular-edge waves propagating along different boundaries, including a free edge, a strip with a weakness stiffness, and a metasurface with a slot array. On the basis of these frameworks, the propagation characteristics of circular-edge waves are revealed, and the rainbow reflection and topological interface state are realized by constructing metasurfaces. Furthermore, the modal frequency prediction, the robustness to structural parameters, and the effective excitation position for circular-edge modes are explored. Finally, based on the above analysis, the customizable local modes are presented, which means that the position of high energy regions in mode shapes can be designed without changing the corresponding modal frequency. Our work provides a new idea for the manipulation of flexural waves in circular plates and find a potential correlation between flexural waves and vibrations, which may exhibit wide applications in vibration control and acoustic device development.

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来源期刊

Applied Mathematical Modelling 数学-工程：综合

CiteScore

9.80

自引率

8.00%

发文量

508

审稿时长

43 days

期刊介绍： Applied Mathematical Modelling focuses on research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. A significant emerging area of research activity involves multiphysics processes, and contributions in this area are particularly encouraged. This influential publication covers a wide spectrum of subjects including heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and system optimization; finite volume, finite element, and boundary element procedures; modelling of inventory, industrial, manufacturing and logistics systems for viable decision making; civil engineering systems and structures; mineral and energy resources; relevant software engineering issues associated with CAD and CAE; and materials and metallurgical engineering. Applied Mathematical Modelling is primarily interested in papers developing increased insights into real-world problems through novel mathematical modelling, novel applications or a combination of these. Papers employing existing numerical techniques must demonstrate sufficient novelty in the solution of practical problems. Papers on fuzzy logic in decision-making or purely financial mathematics are normally not considered. Research on fractional differential equations, bifurcation, and numerical methods needs to include practical examples. Population dynamics must solve realistic scenarios. Papers in the area of logistics and business modelling should demonstrate meaningful managerial insight. Submissions with no real-world application will not be considered.