Transmission and reflection of P wave on the interface between elastic medium and saturated porous medium under nonlocal elastic theory
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摘要:
在工程领域，准确预测波在不同介质中的传播特性对于结构设计和材料性能评估至关重要。经典弹性理论在描述波传播以及处理高频波和多孔介质时存在局限性。为了弥补这一不足，基于非局部弹性理论，探究了P波在弹性介质和饱和多孔介质分界面上的透反射问题。基于非局部介质理论和Helmholtz矢量分解原理，建立了弹性波在层间界面透反射的数学模型，通过数值算例验证了该模型的正确性，并分析了非局部弹性理论下入射频率、入射角度、单一非局部参数、层间非局部参数对分界面处波的透反射振幅比的影响规律。研究结果表明：（1）随着入射波频率的增加，两种理论下的振幅比差异逐渐增大，当频率较高时这种差异性表现尤为显著；（2）在两种理论下，随着角度的增加，反射P1波的振幅比受角度变化的影响最小，其余波型波受角度变化的影响程度相似，其中振幅比最大差异达33%；（3）分界面处波的透反射规律受到非局部参数的调控，弹性介质非局部参数的变化对透射波的振幅比的影响极为微弱。研究成果对于深入理解波在不同介质界面的传播行为具有重要意义，可为复合材料设计、波传播预测及环境振动分析提供理论支撑。
Abstract:Accurate prediction of wave propagation properties in different media is essential for structural design and material performance evaluation in engineering. Classical elasticity theory has limitations in describing wave propagation, particularly when dealing with high-frequency waves and porous media. To address these shortcomings, this study investigated the transmission and reflection of P-waves on the dividing surface of elastic and saturated porous media based on the nonlocal elasticity theory. Based on the nonlocal medium theory and Helmholtz vector decomposition principle, a mathematical model of elastic wave transmission and reflection at the interlayer interface was established, and the correctness of the model was verified by numerical examples. The effects of incident frequency, incident angle, single nonlocal parameter, and interlayer nonlocal parameter on the amplitude ratio of wave transmission and reflection at the interface are analyzed under the nonlocal elastic theory. The results show that the difference between the amplitude ratios under the two theories gradually increases with the increase of the incident wave frequency, becoming particularly pronounced at higher frequencies. The amplitude ratio of the reflected P1 wave presents the least sensitivity to variations in incident angle under both theories, whereas the other wave types demonstrate comparable angular dependencies, with the maximum observed amplitude ratio difference reaching 33%. It is worth noting that the transmission and reflection patterns of waves at the interfaces are regulated by nonlocal parameters, and changes in the nonlocal parameters of the elastic medium have an extremely weak effect on the amplitude ratio of the transmitted waves. The findings of this study are of significance for the in-depth understanding of wave propagation behavior at the interfaces of different media, and provide new theoretical support and analytical tools for engineering applications such as composite material design, wave propagation prediction, and environmental vibration analysis.
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Key words:
- nonlocal elasticity theory /
- porous media /
- elastic wave /
- transparent reflection /
- amplitude ratio
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表 1 饱和土地基物理力学参数
Table 1. Physical and mechanical parameters of saturated soil foundation
材料
参数土颗粒密度/（kg∙m−3） 流体密度/（kg∙m−3） 流体体积模量/GPa 土颗粒体积模量/GPa 土骨架体积模量/MPa 剪切模量/MPa 孔隙率 渗透系数/m−2 流体黏滞系数/（Pa∙s） 弯曲
因子孔隙半径/μm 取值 2 650 1 000 2.25 36 43.6 26.1 0.47 1×10−10 1×10−3 1 23 
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