外磁场调控下偶极梯度半空间中弹性波的反射  

Reflection of Elastic Waves in Dipolar Gradient Half-Space under the Control of External Magnetic Field

作　　者：边鑫禹 李月秋[1] 王长达 BIAN Xinyu;LI Yueqiu;WANG Changda(School of Science,Qiqihar University,Qiqihar 161006,Heilongjiang,China;Key Laboratory of Building Collapse Mechanism and Disaster Prevention,Institute of Disaster Prevention,China Earthquake Administration,Beijing 101601,China)

机构地区：[1]齐齐哈尔大学理学院,黑龙江齐齐哈尔161006 [2]防灾科技学院中国地震局建筑物破坏机理与防御重点实验室,北京101601

出　　处：《力学季刊》2024年第1期200-209,共10页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(12072022);黑龙江省基本业务费专项(135509123);中央高校基本业务费专项(ZY20210211);廊坊市科学技术研究与发展计划自筹经费项目(2021011037)。

摘　　要：本文研究了在偶极梯度弹性固体中,在外加磁场调控作用下,弹性波在界面上的反射问题.当入射波的波长与材料的微结构特征长度近似或者弹性波的频率较高时,材料的微结构效应显著增加.本文首先应用偶极应变梯度理论和麦克斯韦电磁理论推导出弹性波传播的色散方程,然后根据界面条件分别计算出P波入射和SV波入射时各种反射波与入射波的振幅比.最后,根据数值计算结果,讨论了外加磁场以及入射波长对反射波传播的影响.研究结果发现,在偶极梯度弹性固体中,微结构效应可以导致新的波动模式产生和弹性波的色散特征的出现,而外加磁场只是通过洛伦兹力的作用对弹性波传播的速度产生影响,但不会产生新的波动模式和影响弹性波的色散性质.Reflection of elastic waves at the interface of dipolar gradient elastic solids under the control of external magnetic field is studied in this paper.The microstructural effects become more pronounced as the incident wavelength is close to the characteristic length of microstructure or high frequency.Firstly,the dispersion equation of the elastic wave propagation is derived by the dipolar strain gradient theory and Maxwell electromagnetic theory.Then,the reflected-to-incident amplitude ratios of the P-waveand SV-wave incidences are calculated according to the interface conditions.Finally,the influences of the external magnetic field and the wavelength of the incident wave on the propagation of the reflected wave are discussed based on the numerical results.It is found that the microstructural effect can lead to the generation of new wave modes and the appearance of the dispersion characteristics of the elastic wave,while the external magnetic field only affects the velocity of the elastic wave propagation through the Lorentz force,but does not produce new wave modes and affect the dispersion properties of the elastic wave.

关 键 词：偶极应变梯度 微结构效应 洛伦兹力 反射 

分 类 号：O347.41[理学—固体力学] O441[理学—力学]