摘要颗粒材料是一类具有宏观尺寸的离散颗粒组成的集合体，颗粒之间只有在发生形变时 才会产生相互作用，传统的连续介质中的电磁波和声波的平面波理论和多重散射理论等 不再适用，进一步认识声波在颗粒链体系中的传播特性具有重要的基础理论和应用价值 研究意义。本文采用离散元方法模拟研究了孤立波在对称 Y 型颗粒链中的叠加特性。研 究发现，孤立波的波速和能量均以非线性方式叠加。当枝杈链与主链的夹角小于 45°时， Y 型颗粒链可等效为重－轻颗粒链；当枝杈链与主链的夹角大于 45°时，Y 型颗粒链可 等效为轻－重颗粒链。对于前者，孤立波的透射系数为 1；对于后者，随着角度的增大， 透射系数减小，反射系数增大。模拟结果与基于准粒子模型的数值预测非常吻合。79971

毕业论文关键词  颗粒物质 离散元方法 孤立波的叠加 准粒子模型 

Title Simulation study on the acoustic diode characteristics   of symmetric Y-shaped granular chain             

Abstract Granular material is an aggregate of discrete particles with macroscopic size, only when the deformation occurs among the particles will they produce the interaction。 The traditional plane wave theory and multiple scattering theory of electromagnetic waves and acoustic waves in the continuous medium are no longer applicable。 Therefore, further understanding of the propagation characteristics of acoustic waves in granular systems has important theoretical and applied value。 We study the superposition of two solitary waves in symmetric Y-shaped granular chain by using discrete element method。 The results show that the wave velocity and energy of solitary wave are superposed in nonlinear way。 when the branch angle between the branches chain and main chain is less than 45°, the symmetric Y-shaped granular chain can be equivalent to the heavy-light composite granular chain; and when the branch angle is more than 45°, the Y-shaped chain can be equivalent to the light-heavy composite chain。 For the former, the transmission coefficient of solitary wave is 1; for the latter, with the increase of the angle, the transmission coefficient decreases and the reflection coefficient increases。 Analytic predictions based on the quasiparticle model are found to be in excellent agreement with the numerical simulation data。 

Keywords granular material, discrete element method, superposition of solitary wave, quasiparticle model

本科毕业设计说明书 第Ⅰ页

目 次

1     引言 1

1。1    研究背景及意义  1 

1。2    颗粒链中声波传播的研究进展  1 

1。3    小结  8 

2     计算模型  9 

2。1    模拟体系  9 

2。2    计算方法  9 

3     理论模型  11 

3。1    准粒子模型  11 

3。2    对称 Y  型颗粒链的准粒子模型  11 

4    模拟结果与讨论  13 

4。1    模拟结果  13 

4。2 模拟结果的讨论分析  17 结论  19 致谢  20 参考文献  21 

1 引言

1。1 研究背景及意义

颗粒物质一般指由尺寸� > 1μm的颗粒组成的宏观体系[1,2]。小到海岸边的砂石、丰收的 粮食、工厂的原料，大到极区的冰川、地壳的岩块，颗粒物质早已为人所熟知。而且在工农