基于超材料的周期管道系统弯曲波带隙分析及控制

doi:10.16553/j.cnki.issn1000-985x.2024.0253

摘要/Abstract

摘要： 管道系统广泛应用于工业领域,为有效控制管道中的振动,本文设计了一种安装单自由度谐振器的周期管道结构,研究了弯曲波的传播特性。采用传递矩阵法结合Bloch定理推导出传输常数和频率之间的色散关系,并通过有限元仿真验证了能带结果。结果表明,在0~250 Hz存在3个禁带和3个通带,其中第一通带频率范围非常窄,而第二和第三通带频率范围较宽。为了分析管道参数对振动传递特性的影响,采用控制变量法分别对单胞长度、管厚和内径尺寸等进行了参数分析。结果表明,单胞长度的增加会缩小带隙宽度,而管厚和内径尺寸的增加则会扩大带隙宽度。最后,为实现对通带宽度的控制,引入单自由度谐振器,对特定通带进行有效控制,并通过有限元分析确定谐振器的最佳安装位置。结果表明,谐振器对通带宽度具有显著的缩减效果。研究结果为管道结构振动控制提供了理论支持,并可应用于低频振动隔离设计中。

关键词: 声学超材料, 周期管道系统, 弯曲波, 带隙, 谐振器, 传递矩阵法, 振动传递率

Abstract: Pipeline systems are widely used in industrial fields. To effectively control the vibration of the pipes, a periodic pipeline structure with a single degree-of-freedom resonator was designed in this paper, and the propagation characteristics of flexural waves were investigated. The dispersion relationship between the transmission constant and frequency was derived using the transfer matrix method combined with Bloch’s theorem, and the bandgap results were verified through finite element simulation. The results indicate that there are three bandgaps and three passbands within the frequency range of 0~250 Hz, with the first passband having a very narrow frequency range, the second and third passbands having a wider frequency range. In order to interpret the influence of pipeline parameters on transmission characteristics, the control variable method was used to analyze parameters such as unit cell length, pipe thickness, and inner diameter size. The results indicate that an increase in the unit cell length leads to a reduction in bandgap width, while increases in pipe thickness and inner diameter result in an expansion of bandgap width. Finally, to achieve control over the passbands, a single degree-of-freedom resonator was introduced to effectively control specific passbands, and the optimal installation position of the resonator was determined through finite element analysis. The results show that the resonator significantly reduces the width of the passbands. This study provides theoretical support for vibration control of pipeline structures, and can be applied to the design of low-frequency vibration isolation.

Key words: acoustic metamaterial, periodic pipeline system, flexural wave, bandgap, resonator, transfer matrix method, vibration transmission

中图分类号:

O735

李小双, 蒋帅, 郭振坤. 基于超材料的周期管道系统弯曲波带隙分析及控制[J]. 人工晶体学报, 2025, 54(4): 589-597.

LI Xiaoshuang, JIANG Shuai, GUO Zhenkun. Flexural Waves Band Gap Analysis and Control in Metamaterial-Based Periodic Pipeline Systems[J]. Journal of Synthetic Crystals, 2025, 54(4): 589-597.

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