类固态颗粒物质的声波性质研究
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摘要
颗粒物质指由大量离散态颗粒组成的堆积体,是自然界最为广泛存在的、人们非常熟悉的物质类型之一。它具有许多复杂的物理性质,如非线性、塑性变形、能量耗散、类固-液态转换、等等,是当前软凝聚态物理领域里的一个重要研究对象。由于许多工业和环境保护领域都涉及到颗粒物质,这一物理研究方向也与它们密切相关。近年来在这方面的一些研究报道显示,紧密堆积的类固态颗粒物质内部应力的分布、静态屈服、和声波传播等所有宏观静力学问题都可在经典弹性理论的框架下,用一个弹性势能模型来统一描述。为了进一步深入考察这个观点的正确性,本文从其给出的弹性势能模型出发,对当前该领域关注的一些声波现象进行了理论分析。论文重点计算了倾斜颗粒层的应力可能出现的各种不同状态,及其对表面声波性质的影响。结果发现,不同应力下的表面波性质相差不大。这意味着上述弹性理论观点不会与已有的表面波测量数据冲突。具体地,本文基于这个弹性势能模型,开展了如下内容的工作：
首先,系统分析了均匀应力状态颗粒固体的平面波问题。给出了圆柱对称时,沿对称轴方向和垂直对称轴方向传播的平面波速度的解析表达式,并与现有的实验测量结果进行了比较讨论。理论能很好地符合现有文献报道的声速实验数据,特别是能够解释观测到的径向横波简并劈裂现象。这些公式能用于分析处理平面波波速的实验结果,或者用于从实验数据反演势能模型中的材料参数值。论文对后者给出了一套完整的反演方案步骤。
其次,论文给出了重力固结下无限大倾斜颗粒层的所有可能应力分布的、含三个积分常数的通解,及其力学稳定性分析。其中积分常数不为零的解在以前未曾研究过,它们的主要特点是在最大倾斜角时颗粒层不是整体同时、而是从顶部的自由表面处开始失去稳定。这一结果表明弹性理论可以正确地反映与颗粒物质表面崩塌,或表面流动等局域屈服有关现象。
最后,论文计算了上述应力非均匀颗粒层的表面波性质,主要是实验可直接观测的性质,包括传播模式和频散关系等。研究发现取决于积分常数值,这些表面波可以解耦成纵向模式(sagittal mode)和横向模式两类,但它们也可能因发生耦合而不能分开。分析并给出了这两类表面波模式之间发生耦合与分离的条件。另外数值计算显示,颗粒层应力状态的不同对这些表面波性质有一定的影响,但强度不大。鉴于目前的实验精度还远不能分辨这个细节,弹性理论对表面波的有效性仍可以继续保持。
随着对颗粒物质宏观物理认识的逐步深入,今后有关弹性势能的考察工作将会更多地关注于理论和实验的细节对比,以及整体的协调性上。论文对声学在这方面的独特优势和存在的问题,特别是目前还未能澄清的、描述表面波时的势能参数值与描述其他力学实验时的参数值不协调问题,进行了简单讨论和展望。
Granular materials are large conglomerations of discrete macroscopic particles and widely spread both in nature and our daily life. They may exhibit many complex physical behaviors including nonlinearity, plastic deformation, energy dissipation, quasi-solid-liquid transition, and so on. Therefore, granular matter is an important research subject in the field of soft condensed matter physics at present, which is also closely related with many fields of industry and environmental protection. Recent studies have suggested all macroscopic statics problems, including static stress distribution, mechanical yield, and sound propagation for dense granular media, could be analyzed by an elastic potential model in the framework of classical elasticity theory. To further investigate the correctness of this viewpoint, theoretical studies of some acoustic phenomena concerned currently are performed with this elastic potential model. This thesis focuses on the calculation of various stress states that may occur in an inclined granular layer, and their influences on surface waves propagation. Results indicate that different stresses have little effect on the properties of surface waves. This means that the elasticity theory mentioned above does not conflict with existing experimental data of surface waves. Based on this elastic potential model, the concrete contents of this thesis are listed as follows:
Firstly, the issue of plane wave propagation in uniform stressed granular solid has been systematic analyzed. For case of samples with cylindrical symmetry, the analytic expressions of velocities of plane waves propagating along and perpendicular to the symmetry axis are derived, and compared with the available experimental data. It is found that the theoretical predictions are in agreement well with the measurements of sound velocity, and can explain the degenerate splitting phenomenon of transverse waves velocity traveling along the radial direction.These formulas may be used to analyze the experimental results of plane-wave velocities or obtain the parameter values of the elastic potential model from experimental data. A complete inverse scheme is designed for the latter.
Secondly, the present work gives a general solution of stress distributions with three integral constants, and stability analysis of an inclined granular layer at rest under gravity. It has never been studied that the integral constants in general solution are not all equal to zero, a striking feature of which is the onset of instability occurred only at a free surface rather than in whole layer. Results show that the elasticity theory could be used for accounting those local yield phenomena such as surface avalanches and flows of granular layers.
Finally, we calculate the surface wave propagation characteristics, the main of which can be directly observed by experiment, including the shape of the modes and their dispersion relation in the above-mentioned non-uniform stressed granular layer. Depending on integral constants, there have two types of surface waves, namely sagittal and transverse modes. The condition of coupling between them is discussed. In addition, numerical calculations show that different initial stress states produce certain influence on the propagation properties of surface waves, but the intensity is not great. Since the present experimental accuracy is far from being able to distinguish this detail, the validity of elasticity theory on the surface wave can still be maintained.
With the deepening of understanding of macroscopic physics of granular matter, investigations of the elastic potential energy will pay more attention to the details of the comparison between theoretical and experimental results, and the coordination on entirety. The special advantages of sound waves in this research and the problems, especially the discrepancy of parameters values between describing surface waves and other mechanical experiments are discussed at last.
首先,系统分析了均匀应力状态颗粒固体的平面波问题。给出了圆柱对称时,沿对称轴方向和垂直对称轴方向传播的平面波速度的解析表达式,并与现有的实验测量结果进行了比较讨论。理论能很好地符合现有文献报道的声速实验数据,特别是能够解释观测到的径向横波简并劈裂现象。这些公式能用于分析处理平面波波速的实验结果,或者用于从实验数据反演势能模型中的材料参数值。论文对后者给出了一套完整的反演方案步骤。
其次,论文给出了重力固结下无限大倾斜颗粒层的所有可能应力分布的、含三个积分常数的通解,及其力学稳定性分析。其中积分常数不为零的解在以前未曾研究过,它们的主要特点是在最大倾斜角时颗粒层不是整体同时、而是从顶部的自由表面处开始失去稳定。这一结果表明弹性理论可以正确地反映与颗粒物质表面崩塌,或表面流动等局域屈服有关现象。
最后,论文计算了上述应力非均匀颗粒层的表面波性质,主要是实验可直接观测的性质,包括传播模式和频散关系等。研究发现取决于积分常数值,这些表面波可以解耦成纵向模式(sagittal mode)和横向模式两类,但它们也可能因发生耦合而不能分开。分析并给出了这两类表面波模式之间发生耦合与分离的条件。另外数值计算显示,颗粒层应力状态的不同对这些表面波性质有一定的影响,但强度不大。鉴于目前的实验精度还远不能分辨这个细节,弹性理论对表面波的有效性仍可以继续保持。
随着对颗粒物质宏观物理认识的逐步深入,今后有关弹性势能的考察工作将会更多地关注于理论和实验的细节对比,以及整体的协调性上。论文对声学在这方面的独特优势和存在的问题,特别是目前还未能澄清的、描述表面波时的势能参数值与描述其他力学实验时的参数值不协调问题,进行了简单讨论和展望。
Granular materials are large conglomerations of discrete macroscopic particles and widely spread both in nature and our daily life. They may exhibit many complex physical behaviors including nonlinearity, plastic deformation, energy dissipation, quasi-solid-liquid transition, and so on. Therefore, granular matter is an important research subject in the field of soft condensed matter physics at present, which is also closely related with many fields of industry and environmental protection. Recent studies have suggested all macroscopic statics problems, including static stress distribution, mechanical yield, and sound propagation for dense granular media, could be analyzed by an elastic potential model in the framework of classical elasticity theory. To further investigate the correctness of this viewpoint, theoretical studies of some acoustic phenomena concerned currently are performed with this elastic potential model. This thesis focuses on the calculation of various stress states that may occur in an inclined granular layer, and their influences on surface waves propagation. Results indicate that different stresses have little effect on the properties of surface waves. This means that the elasticity theory mentioned above does not conflict with existing experimental data of surface waves. Based on this elastic potential model, the concrete contents of this thesis are listed as follows:
Firstly, the issue of plane wave propagation in uniform stressed granular solid has been systematic analyzed. For case of samples with cylindrical symmetry, the analytic expressions of velocities of plane waves propagating along and perpendicular to the symmetry axis are derived, and compared with the available experimental data. It is found that the theoretical predictions are in agreement well with the measurements of sound velocity, and can explain the degenerate splitting phenomenon of transverse waves velocity traveling along the radial direction.These formulas may be used to analyze the experimental results of plane-wave velocities or obtain the parameter values of the elastic potential model from experimental data. A complete inverse scheme is designed for the latter.
Secondly, the present work gives a general solution of stress distributions with three integral constants, and stability analysis of an inclined granular layer at rest under gravity. It has never been studied that the integral constants in general solution are not all equal to zero, a striking feature of which is the onset of instability occurred only at a free surface rather than in whole layer. Results show that the elasticity theory could be used for accounting those local yield phenomena such as surface avalanches and flows of granular layers.
Finally, we calculate the surface wave propagation characteristics, the main of which can be directly observed by experiment, including the shape of the modes and their dispersion relation in the above-mentioned non-uniform stressed granular layer. Depending on integral constants, there have two types of surface waves, namely sagittal and transverse modes. The condition of coupling between them is discussed. In addition, numerical calculations show that different initial stress states produce certain influence on the propagation properties of surface waves, but the intensity is not great. Since the present experimental accuracy is far from being able to distinguish this detail, the validity of elasticity theory on the surface wave can still be maintained.
With the deepening of understanding of macroscopic physics of granular matter, investigations of the elastic potential energy will pay more attention to the details of the comparison between theoretical and experimental results, and the coordination on entirety. The special advantages of sound waves in this research and the problems, especially the discrepancy of parameters values between describing surface waves and other mechanical experiments are discussed at last.
引文
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