Phononic Band Gap Systems in Structural Mechanics: Finite Slender Elastic Structures and Infinite Periodic Waveguides
Phononic Band Gap Systems in Structural Mechanics: Finite Slender Elastic Structures and Infinite Periodic Waveguides
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DOI：
10.1115/1.4023819
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发表时间：
2013-08
期刊：
影响因子：
--
通讯作者：
M. Brun;A. Movchan;I. Jones
中科院分区：
文献类型：
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作者：
M. Brun;A. Movchan;I. Jones
本文提出了一种新的谱方法，并给出了一个渐近模型，并对长桥或高层建筑等细长弹性系统进行了数值模拟。重点讨论了可能在无限周期波导中传播的Bloch波解的渐近逼近。虽然被动质量阻尼器的概念在工程文献中是常规的，但对于分析长而有限的细长弹性系统来说，无限大的波导问题并不明显。对Bloch波的形式数学处理将归结为对周期结构的基本单元上的运动方程的谱分析，并在单元的边界上施加Bloch-Floket准周期条件。某些类型的驻波的频率可以用解析的方法估计。论文讨论的应用之一是横跨伏尔加河的伏尔加河上的“舞桥”。
The paper presents a novel spectral approach, accompanied by an asymptotic model and numerical simulations for slender elastic systems such as long bridges or tall buildings. The focus is on asymptotic approximations of solutions by Bloch waves, which may propagate in a infinite periodic waveguide. Although the notion of passive mass dampers is conventional in the engineering literature, it is not obvious that an infinite waveguide problem is adequate for analysis of long but finite slender elastic systems. The formal mathematical treatment of a Bloch wave would reduce to a spectral analysis of equations of motion on an elementary cell of a periodic structure, with Bloch–Floquet quasi-periodicity conditions imposed on the boundary of the cell. Frequencies of some classes of standing waves can be estimated analytically. One of the applications discussed in the paper is the “dancing bridge” across the river Volga in Volgograd.