颗粒物质在非对称周期结构中的运动

The granular materials are closely related with industrial production and people's daily life. The research on the granular materials has been a hot field of the international frontier. This project will focus on the motions of the granular materials within asymmetric periodic structures under external excitation with the method of experiments. A vertically excited two-dimensional annular granular system with an asymmetric periodic sawtooth-shaped base will be adopted in the experiments. The research will include: (1) Surface waves of the granular system. We will study the influence of system parameters, such as the material of granules, the thickness of granular layer, and different asymmetric periodic structures of the sawtooth-shaped base, etc., on the surface waves; generate more detailed phase diagrams; conclude a dispersion relation of the surface waves in which the system parameters are considered; (2) Internal flow of the granular system. We will mainly study the variation of horizontal flow with time, space, and excitation parameters under different system parameters; especially study the relation between the surface waves and the internal flow; preliminarily establish a quantitative relation; (3) Internal shock waves of the granular system. We will analyze the formation and propagation of the shock waves; study the influence of system parameters and excitation parameters on the shock waves; especially study the motion law of the granular system when the three completely different motions, i.e. the surface wave, the internal flow and the internal shock wave, exist simultaneously. The intensive research on these phenomena will have important meanings to develop the theory of the granular materials, and to guide practice better.

颗粒物质与工业生产及人们的日常生活密切相关，近几十年来已成为国际前沿热门研究领域。本项目将致力于通过实验研究外界激励下颗粒物质在非对称周期机构中的运动。实验拟采用垂直激励下底部有非对称锯齿结构的二维环形颗粒系统。研究内容包括：（1）颗粒系统的表面波动。研究颗粒材质、颗粒层厚、不同齿形的底部结构等系统参数对表面波动的影响，作出更详细的波动相图，总结出包含系统参数影响项的色散关系；（2）颗粒系统的内部流动。主要研究不同系统参数下水平流动随时间、空间以及激励参数的变化，重点研究内部流动和表面波动之间的相互关联，初步建立定量关系；（3）颗粒系统的内部激波。分析激波的形成及传播过程，研究系统参数和激励参数对激波的影响，重点研究当表面波动、内部流动以及内部激波这三种完全不同的运动形式同时存在时颗粒系统的运动规律。对这些现象做深入研究，对于进一步发展颗粒物质理论，以及更好地指导实践问题，将有着重要意义。

颗粒物质在自然界、工业生产及人们的日常生活中广泛存在，对颗粒物质的研究不仅能促进非线性物理理论的发展，还能更好地指导实践，改善人们的生活。申请人前期的研究工作表明在垂直振动下颗粒物质有表面波动和内部流动。本项目在前期工作的基础上通过实验研究了颗粒物质在非对称周期结构中的运动。主要内容包括：（1）颗粒系统的表面波动。研究了颗粒材质、颗粒层厚、不同周期结构等对表面波动的影响，做出了更详细的波动相图；（2）颗粒系统的内部流动。研究了不同系统中水平流动随时空以及振动参数的变化，内部流动和表面波动之间的相互关联，重点研究了流动共振，即流动在某些参数下达到最大值；（3）颗粒系统的内部激波。分析了激波的形成和传播过程，研究了各参数对激波的影响，重点研究了激波作为机械波的多普勒效应。本项目的研究为颗粒物质积累了丰富的实验现象和实验数据，为理论建设提供了实验依据。