基于压电分流技术的PT对称梁散射特性研究

Study on Scattering Characteristic of PT Symmetric Beam Based on Piezoelectric Shunting Technology

为了解决宇称-时间(Parity-Time,PT)对称结构存在结构复杂、奇异点难以调谐的问题,基于压电分流技术,设计一种针对弯曲波的PT对称梁.推导PT对称条件,基于等效介质法和有限元法,验证所设计增益单元、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.通过传递矩阵法和有限元法,对PT对称梁的散射特性进行分析,讨论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511 Hz和520.5 Hz在内的多个奇异点.弯曲波频率为511 Hz的弯曲波从右端入射时反射系数趋于零,而弯曲波频率为520.5 Hz时,它必须施加在左端从而达到完全透射而不产生反射.

To solve the problems of complex structure and difficulty in tuning the exceptional points in the exist⁃ing PT-symmetric structures,a PT-symmetric beam for flexural waves is designed based on piezoelectric shunting technology.Firstly,the PT-symmetric condition is derived.Then,based on the effective medium method and finite el⁃ement simulation,it is verified that the effective parameters of the gain and loss unit meet the PT-symmetric condi⁃tion,and the tunability of exception points is studied by changing the resonant frequency and the shunting resistance.Finally,the scattering property of the PT-symmetric beam is derived by the transfer matrix method and finite element simulation,and the relationship between exceptional points and unidirectional non-reflection is illustrated.The cal⁃culated and simulated results show that the PT-symmetric beam has several exceptional points including 511 Hz and 520.5 Hz.When the incident flexural wave of 511 Hz is applied at the right side of the PT-symmetric beam,the re⁃flection coefficient is close to zero.However,when the frequency of the incident flexural waves changes to 520.5 Hz,it should be applied on the left side of the PT-symmetric beam to gain an entire transmission without reflection.