Researches On Properties Of Sound Waves In Solid-like Granular Matter

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.