李梁娟, 张博, 禹建功,等.一维六方准晶板中Lamb波特性研究[J].河南理工大学学报（自然科学版）,2022,41(6):130-136.

LI L J, ZHANG B, YU J G,et al.Study on Lamb wave characteristics in the 1-D hexagonal quasi-crystal plate[J].Journal of Henan Polytechnic University(Natural Science) ,2022,41(6):130-136.

一维六方准晶板中Lamb波特性研究

李梁娟1, 张博2, 禹建功2, 张小明2

1.河南理工大学 数学与信息科学学院，河南 焦作，454000；2.河南理工大学 机械与动力工程学院，河南 焦作，454000

摘要:准晶材料结构在制备过程中会出现裂缝、夹杂等缺陷，超声导波具有多模态和频散特性，能够很好识别结构中的微细裂纹等缺陷，但应用超声导波无损检测技术的先决条件是深刻认识结构中导波的传播与衰减特性。基于此，提出一种改进的勒让德多项式级数法，无需迭代便能得到Bak模型和弹性/流体动力学模型下波动力学方程的解析解。计算得到一维六方准晶板中Lamb波的频散曲线、声子和相子场位移分布，研究两种模型下声-相耦合效应对波动特性的影响。结果表明：Bak模型中声-相耦合效应对声子模态有微弱影响，对相子模态有显著影响；弹性/流体动力学模型中声-相耦合效应对不传播的相子模态有显著影响，对声子模态没有影响。所得结果为一维六方准晶板的导波无损检测提供了一定的理论基础。

关键词:准晶;Lamb波;声-相耦合效应;频散曲线;位移分布

doi:10.16186/j.cnki.1673-9787.2021040003

基金项目:国家自然科学基金资助项目（U1804134，51975189，12102131 ）；河南理工大学博士基金资助项目（B2021-32）

收稿日期:2021/04/09

修回日期:2021/09/18

出版日期:2022/11/25

Study on Lamb wave characteristics in the 1-D hexagonal quasi-crystal plate

LI Liangjuan1, ZHANG Bo2, YU Jiangong2, ZHANG Xiaoming2

1.School of Mathematics and Information Science， Henan Polytechnic University， Jiaozuo 454000， Henan， China；2.School of Mechanical and Power Engineering， Henan Polytechnic University， Jiaozuo 454000， Henan， China

Abstract:Due to its high brittleness，quasi-crystal structures are very sensitive to defects in the material preparation，such as cracks and inclusions.Ultrasonic guided waves are of multi-mode and dispersion characteristics，and can be used to identify the micro-cracks and other defects in the structure.However，the prerequisite utilizing them is a deep understanding of their propagation and attenuation characteristics.Accordingly，wave dynamic equations were derived in the context of the Bak’s and elastohydrodynamic models.An improved Legendre polynomial series approach was developed to obtain analytic solutions without iteration.The dispersion curves，phonon，and phason displacement distributions of Lamb wave in the 1-D hexagonal quasi-crystal plate were illustrated.The phonon-phason coupling effect on the wave characteristics was investigated.The results demonstrated that，the phonon-phason coupling effect in the context of the Bak’s model on phonon modes was extremely weak，and significant on phason modes；The phonon-phason coupling effect in the context of elastohydrodynamic model had significant influence on the non-propagating phason modes，without affecting phonon modes.A theoretical basis for the guided wave non-destructive testing on 1-D hexagonal quasi-crystal plates was provided by the results.

Key words:quasi-crystal;Lamb wave;phonon-phason coupling effect;dispersion curve;displacement distribution

 015_2021040003_李梁娟_H.pdf