张小明, 陈滔, 周红梅, 等.压电半导体板超声导波特性研究[J].河南理工大学学报（自然科学版）,2023,42(1):95-101.

ZHANG X M, CHEN T, ZHOU H M, et al.Study on the characteristics of ultrasonic guided wave in a piezoelectric semiconductor plate[J].Journal of Henan Polytechnic University(Natural Science) ,2023,42(1):95-101.

压电半导体板超声导波特性研究

张小明, 陈滔, 周红梅, 禹建功

河南理工大学 机械与动力工程学院，河南 焦作 454000

摘要:利用解析Legendre多项式方法研究压电半导体板中的超声导波特性，该方法将传统Legendre多项式法计算波动力学问题时存在的大量数值积分转换为解析积分计算，克服了传统方法计算量大、计算耗时的问题。导出不同电学边界下的压电半导体板耦合波动方程，利用解析Legendre多项式法将耦合波动方程转换为以波数为特征值的特征计算问题，得到超声导波频散关系。计算压电半导体板SH波频谱，并与文献结果对比验证所提方法的正确性。研究压电半导体板Lamb波的相速度频散、衰减和应力分布，分析电学边界条件和稳态载流子浓度对相速度频散和衰减的影响及稳态载流子浓度对应力分布的影响。数值结果表明：电学边界条件和稳态载流子浓度对压电半导体板Lamb波相速度和衰减有较为显著的影响，调节稳态载流子浓度可以实现超声导波特性的调控。

关键词:压电半导体;Legendre多项式法;解析积分;相速度;衰减

doi:10.16186/j.cnki.1673-9787.2021070032

基金项目:国家自然科学基金资助项目（U1504106）；河南省高校青年骨干教师培养计划项目（2018-GGJS-060）；河南理工大学创新型科研团队项目（T2022-4）

收稿日期:2021/07/07

修回日期:2021/10/07

出版日期:2023/01/25

Study on the characteristics of ultrasonic guided wave in a piezoelectric semiconductor plate

ZHANG Xiaoming, CHEN Tao, ZHOU Hongmei, YU Jiangong

School of Mechanical and Power Engineering，Henan Polytechnic University，Jiaozuo 454000，Henan，China

Abstract:The characteristics of ultrasonic guided wave in a piezoelectric semiconductor plate were investigated by using the analytical Legendre polynomial method.The presented method converted a large number of numerical integrals existing in the traditional Legendre polynomial method to the analytical integral calculation，which overcame the shortcomings of large amount of calculation and time-consuming.The coupled wave equations of piezoelectric semiconductor plate with different electrical boundaries were derived and transformed into the characteristic calculation problem with wave number as eigenvalue using the presented method，and then the dispersion relation was obtained.To validate the presented method，the spectrum of SH wave in a piezoelectric semiconductor plate was calculated and compared with the available literature results.The phase velocity dispersion，attenuation and stress distribution of Lamb wave in a piezoelectric semiconductor plate were studied.The effects of electrical boundary conditions and steady-state carrier density on phase velocity dispersion and attenuation，and the effects of steady-state carrier density on stress distribution were illustrated.The numerical results showed that the electrical boundary conditions and steady-state carrier density had significant effects on the Lamb wave phase velocity and attenuation，and the ultrasonic guided wave characteristics could be regulated by adjusting the steady-state carrier density.

Key words:piezoelectric semiconductor;Legendre polynomial method;analytical integral;phase velocity;attenuation

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