Reflection of Elastic Waves at Imperfect Interface in a Couple-Stress Half-Space Under the External Magnetic Field
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摘要: 研究了外磁场调控下弹性波在偶应力固体中弹性界面处的反射问题.首先, 应用偶应力理论和Maxwell电磁学理论推导出了弹性波传播的控制方程和三种波(P波、SV波和SS波), 并且发现外磁场会通过Lorentz力对弹性波的传播产生影响, 但不会产生新的波动模式. 其次, 根据弹性界面条件得到相应线性代数方程组, 推导出了P波和SV波入射时各种反射波相对于入射波的振幅比. 然后，用能流比定义反射系数, 讨论了P波入射时外磁场、3个弹性常数、偶应力参数和入射波的角频率对弹性波反射系数的影响. 最后, 通过各波的法向能量守恒检验了数值结果的准确性Abstract: The reflection problem of elastic waves at the elastic interface in couple-stress solids was studied under the influence of an external magnetic field. Firstly, based on the couple stress theory and Maxwell's electromagnetic theory, the governing equations for the propagation of elastic waves and 3 types of waves (the P wave, the SV wave and the SS wave) were derived. It was also found that the external magnetic field affects the propagation of elastic waves through the Lorentz force, but no new wave patterns are generated. Secondly, based on the elastic interface conditions, the corresponding linear algebraic equations were obtained, and the amplitude ratios of various reflected waves relative to the incident wave in the case of incident P waves and SV waves were derived. Then, the reflection coefficient was defined with the energy flow ratio, and the effects of the external magnetic field, 3 elastic constants, couple stress parameters, and the angular frequency of the incident wave on the elastic wave reflection coefficient, were discussed for the incident P wave. Finally, the accuracy of the numerical results was verified through the conservation of normal energy for each wave.
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Key words:
- external magnetic field /
- couple stress /
- elastic interface /
- reflection /
- energy conservation
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图 1 外磁场作用下入射P波和SV波在偶应力固体半空间非完好界面的反射
Figure 1. Reflection of the incident P wave and SV wave at the incomplete boundary of a couple stress solid half-space under the external magnetic field
图 2 P波入射时外磁场H0对反射系数的影响
Figure 2. Influences of external magnetic field H0 on the reflection coefficients in the incident P wave situation
图 3 P波入射时法向弹性常数Kn对反射系数的影响
Figure 3. Influences of normal stiffness Kn on the reflection coefficients in the incident P wave situation
图 4 P波入射时切向弹性常数Kτ对反射系数的影响
Figure 4. Influences of tangent stiffness Kτ on the reflection coefficients in the incident P wave situation
图 5 P波入射时旋转弹性常数Kg对反射系数的影响
Figure 5. Influences of rotational stiffness Kg on the reflection coefficients in the incident P wave situation
图 6 P波入射时偶应力参数η对反射系数的影响
Figure 6. Influences of couple-stress constant η on the reflection coefficients in the incident P wave situation
图 7 P波入射时角频率ω对反射系数的影响
Figure 7. Influences of angular frequency ω on the reflection coefficients in the incident P wave situation
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