Bandgap structure of tensegrity mass–spring chains equipped with internal resonators

IF 1.9 4区工程技术 Q3 MECHANICS

Mechanics Research Communications Pub Date : 2024-04-13 DOI:10.1016/j.mechrescom.2024.104273

Luca Placidi , Julia de Castro Motta , Fernando Fraternali

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Abstract

This work studies the dispersion relation of a Maxwell type mass–spring chain formed by lumped masses and the parallel arrangement of two different types of tensegrity prisms. Use is made of the Bloch–Floquet theory of discrete systems in association with a linearized model of the response of the tensegrity units under compression loading. Such a modeling is aimed at studying the propagation of compression waves under small perturbations of the initial equilibrium state of the system. For a given value of the cable’s prestress, the tensegrity systems connecting the lumped masses react as elastic springs, which exhibit axial deformations accompanied by relative twisting rotations of the terminal bases. The twisting motion of the chain affects the expression of the kinetic energy, and is accounted for by introducing a suitable definition of equivalent masses. The bandgap structure of the analyzed system is analytically determined and numerical results are obtained for a chain formed by physical models tensegrity $θ = 1$ prisms aligned in parallel with minimal tensegrity prisms. The given results highlight the highly tunable frequency bandgap properties of tensegrity mass–spring chains exhibiting internal resonance capabilities.

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配备内部谐振器的张力质量弹簧链的带隙结构

本论文研究了由块状质量和平行排列的两种不同类型的张拉实体棱柱构成的麦克斯韦质量弹簧链的分散关系。研究利用了离散系统的布洛赫-弗洛克特理论，并结合了张拉实体单元在压缩载荷下的线性化响应模型。这种模型旨在研究压缩波在系统初始平衡状态的微小扰动下的传播。对于给定的缆索预应力值，连接块状质量的张拉系统会像弹性弹簧一样发生反应，表现出轴向变形，并伴随着终端基座的相对扭曲旋转。链的扭转运动影响动能的表达，可通过引入适当的等效质量定义加以解释。分析系统的带隙结构是通过分析确定的，并获得了由物理模型张弦θ=1棱柱与最小张弦棱柱平行排列形成的链的数值结果。所给出的结果凸显了张弦质量弹簧链具有高度可调的频带隙特性，表现出内部共振能力。

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

Mechanics Research Communications 物理-力学

CiteScore

4.10

自引率

4.20%

发文量

114

审稿时长

9 months

期刊介绍： Mechanics Research Communications publishes, as rapidly as possible, peer-reviewed manuscripts of high standards but restricted length. It aims to provide: • a fast means of communication • an exchange of ideas among workers in mechanics • an effective method of bringing new results quickly to the public • an informal vehicle for the discussion • of ideas that may still be in the formative stages The field of Mechanics will be understood to encompass the behavior of continua, fluids, solids, particles and their mixtures. Submissions must contain a strong, novel contribution to the field of mechanics, and ideally should be focused on current issues in the field involving theoretical, experimental and/or applied research, preferably within the broad expertise encompassed by the Board of Associate Editors. Deviations from these areas should be discussed in advance with the Editor-in-Chief.