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基于压电分流技术的PT对称梁散射特性研究
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湖南大学汽车车身先进设计制造国家重点实验室

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国家自然科学基金资助项目(11772123)


Research on scattering characteristic of PT?symmetric beam based on piezoelectric shunting technology
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State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University

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National Natural Science Foundation of China(11772123)

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    摘要:

    非对称传输机制,对弹性波的增强传感、放大及非对称控制来说至关重要。而宇称-时间(Parity-Time,PT)系统有望提供一种简单的解决方案。PT对称系统这一概念来源于量子力学,其特性之一就是单向无反射。本文基于压电分流技术,设计了一种针对弯曲波的PT对称梁。首先推导了PT对称条件,之后基于等效介质法和有限元法,验证了所设计增益、损耗单元的等效参数满足该PT对称条件,并通过改变谐振频率和分流电阻研究了奇异点的可调性。最后通过传递矩阵法和有限元法,对PT对称梁的散射特性进行了分析计算,并讨论了单向无反射点与奇异点之间的关系。理论计算和仿真结果表明,PT对称梁有包括511Hz 和520.5Hz在内的多个奇异点。511Hz的弯曲波从右端入射时反射系数趋于零,而弯曲波频率为520.5Hz时,它必须施加在左端从而达到完全透射而不产生反射。本文所提出PT对称梁具有结构简单、奇异点可调的特点,能较好地实现弯曲波的非对称传输。

    Abstract:

    The mechanism for asymmetric transmission is an important issue for enhanced sensing, amplification and asymmetric control of elastic waves. Parity-Time symmetric systems may provide a simple solution. The concept of Parity-Time symmetric systems comes from quantum mechanics, and one of its characteristics is unidirectional reflectionlessness. A PT symmetric beam for flexural waves is designed, which is based on piezoelectric shunting technology. Firstly, the PT symmetric condition is derived. Then, based on the effective medium method and finite element simulation, it is verified that the effective parameters of gain and loss unit meet the PT symmetric condition. The tunability of exception points is studied by changing the resonant frequency and the shunting resistance. Finally, the scattering property of the PT sym-metric beam is derived by transfer matrix method and finite element simulation, and the relationship between exceptional points and unidirectional non-reflection is illustrated. The calculated and simulated results show that the PT symmetric beam has several exceptional points including 511Hz and 520.5Hz. When the incident flexural waves of 511Hz is applied at the right side of the PT symmetric beam, the reflection coefficient is close to zero. However, when the frequency of the incident flexural waves changes to 520.5Hz, it should be applied on the left side of the PT symmetric beam in order to gain a total transmission without reflecting. The structure of the proposed PT symmetric beam is simple and the exceptional points of it are tunable, which can be used to achieve better asymmetric transmission of flexural wave.

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  • 收稿日期: 2021-06-26
  • 最后修改日期: 2021-10-22
  • 录用日期: 2021-10-27
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