含有周期分布转动振子的声子晶体梁的弯曲振动带隙研究

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振动与冲击 ›› 2017, Vol. 36 ›› Issue (21) : 85-91.

论文

朱学治1，陈照波1，焦映厚1，杨凯2

作者信息 +

Flexural vibration band gaps in phononic crystal beam containing rotational resonators

ZHU Xuezhi 1 CHEN Zhaobo 1 JIAO Yinghou 1 YANG Kai 2

Author information +

文章历史 +

摘要

将转动振子周期布置于基体梁上形成声子晶体梁，受到外激励时，转动振子对基体梁产生动态反力矩作用。基于欧拉梁理论，采用传递矩阵法计算得到含转动振子的声子晶体梁的复能带结构。计算结果表明，转动振子可以使得声子晶体梁产生窄频带局域共振带隙和宽频带Bragg带隙。分析转动振子的转动惯量和转动刚度对带隙的调控作用，得到带隙变化的一般规律。转动刚度恒定时，减小转动惯量会拓宽局域共振带隙。转动振子频率恒定时，过大或过小的转动刚度会减小局域共振带隙带宽。同时提高转动惯量和转动刚度可以有效拓宽Bragg带隙。针对有限长的含转动振子的声子晶体梁，用谱单元法计算振动传递率，验证了含转动振子的声子晶体梁的带隙特性。该研究为声子晶体的带隙设计提供了理论依据。

Abstract

Attach rotational resonators to a host beam to form a phononic crystal beam. Complex band structure of the phononic beam containing rotational resonators was derived though Transfer Matrix Method based on Euler-Bernoulli beam theory. The results showed that narrow band locally resonant band gaps and wide band Bragg band gaps could be achieved by rotational resonators. The effects of rotational resonator parameters, such as rotational stiffness and moment of inertia on the band gaps were analyzed, and general changing law of the band gaps was obtained. Locally resonant band gap could be broadened by minimizing the moment of inertia when the rotational stiffness remains constant. Excessively large or small rotational stiffness could minimize locally resonant band gap while Bragg band gap could be broadened effectively by increasing rotational stiffness and moment of inertia simultaneously. Finally, band gaps property of the phononic crystal beam were verified though transverse vibration transmission calculation using Spectrum Element Method.

导出引用

朱学治1，陈照波1，焦映厚1，杨凯2. 含有周期分布转动振子的声子晶体梁的弯曲振动带隙研究[J]. 振动与冲击, 2017, 36(21): 85-91

ZHU Xuezhi 1 CHEN Zhaobo 1 JIAO Yinghou 1 YANG Kai 2 . Flexural vibration band gaps in phononic crystal beam containing rotational resonators[J]. Journal of Vibration and Shock, 2017, 36(21): 85-91

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