细观非连续介质的应力波传播研究

袁良柱; 陈美多; 谢雨珊; 陆建华; 王鹏飞; 徐松林

doi:10.11883/bzycj-2023-0365

细观非连续介质的应力波传播研究

doi: 10.11883/bzycj-2023-0365

袁良柱^1,,
陈美多¹,
谢雨珊¹,
陆建华¹,
王鹏飞¹,
徐松林^{1, 2, ,}

1.
中国科学技术大学中国科学院材料力学行为和设计重点实验室，安徽合肥 230027
2.
中国地震局地震预测研究所高压物理与地震科技联合实验室，北京 100036

基金项目: 国家自然科学基金 (11672286, 11872361)；高压物理与地震科技联合实验室室开放基金 (2019HPPES01)；中石油与中科院重大战略合作项目(2015A-4812)；中央高校基本科研业务费专项资金(WK2480000008)

详细信息

作者简介:
袁良柱（1998－　），男，博士研究生，ylzustcedu@mail.ustc.edu.cn

通讯作者:
徐松林（1971－　），男，博士，研究员，博士生导师，slxu99@ustc.edu.cn

中图分类号: O347.3
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- 被引次数: 0
出版历程
- 收稿日期: 2023-10-09
- 修回日期: 2023-12-14
- 网络出版日期: 2024-02-04
- 刊出日期: 2024-09-20

Investigation on stress wave propagation in mesoscopic discontinuous medium

1.
CAS Key Laboratory for Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei 230027, Anhui, China
2.
United Laboratory of High-Pressure Physics and Earthquake Science, Institute of Earthquake Forecasting, China Earthquake Administration, Beijing 100036, China

摘要

摘要: 固体介质，如岩石、混凝土、贝壳和多孔材料等均具有细观非连续、宏观连续的特性，揭示这种细观非连续性对材料动力学响应的影响规律，对于材料设计、安全防护等具有重要意义。从广义Taylor公式出发，推导了分数阶定义下的非连续介质的一维波动方程，引入等效分数阶简化了控制方程。利用有限差分法得到了控制方程的数值解，结果表明：控制方程中的等效分数阶阶数越小，计算得到的波形衰减的程度越大。为了验证方程的可靠性，并进一步研究非连续介质的波传播规律，在考虑多孔材料、岩石等介质的结构特征的基础上，基于ABAQUS软件建立了随机多孔介质模型。分析发现：多孔介质的波传播受到介质细观非连续程度、材料属性和输入波脉宽的影响，但对应的等效分数阶阶数只与介质细观非连续程度相关，因此，其可以作为评价非连续介质动态响应的一个依据。等效分数阶阶数随着孔隙率的增加而减小，孔洞相对数量分布大致相同的情况下，其统计关系近似呈线性关系。研究结果可为研究多孔材料、贝壳等细观非连续介质的波动传播提供新思路。
- 分数阶导数 /
- 细观非连续 /
- 波传播 /
- 有限差分 /
- 等效分数阶阶数
Abstract: Solid mediums, like rocks, concretes, shells and porous materials, etc., has the characteristics of microscopic discontinuity and macroscopic continuity. It is of great significance for material design, safety protection and other fields to reveal the influence of the meso-discontinuity on the dynamic response of the material. In this paper, based on the generalized Taylor’s formula under fractional definition, the governing equation of 1-D wave propagation in discontinuous medium is derived. Equivalent fractional order is introduced and the simplified form of the governing equation is presented for easily calculating. By using the finite difference method, the numerical solution of the governing equation is obtained. The influence of equivalent fractional order on wave propagation are analyzed. By the time domain analysis, the smaller the equivalent fractional order, the greater the degree of attenuation of the calculated waveform. By the frequency domain analysis, both high frequency wave and low frequency wave exhibit attenuation, and the attenuation of high frequency wave is higher than that of low frequency wave, which makes the pulse duration of the wave being larger. It is obvious that the equivalent fractional order has a certain relationship with the spatial structure of discontinuous medium. Based on the structural characteristics of some meso-discontinuous medium, e.g., porous materials and rocks, a randomly distributed pores model is established by using ABAQUS to verify the reliability of the governing equation and study the wave propagation of meso-discontinuous medium. The effects of porosity, material properties and input waves on wave propagation are analyzed. The degree of wave attenuation is positively related to the porosity of the medium, and negatively related to the wave velocity and the pulse duration of input wave. However, the equivalent fractional order is only related to the porosity and pore distribution of the discontinuous medium. When the spatial structure of the discontinuous medium remains unchanged, the corresponding equivalent fractional order does not change with the material property and the pulse duration of the input wave. By the randomly distributed pores model with various porosities, it is found that the equivalent fractional order decreases with the increase of porosity. Under the same porosity, the heterogeneity of pore distribution will result in different waveforms, while with the increase of porosity, this difference becomes more obvious, but the corresponding equivalent fractional order only has little difference. The statistical relation between equivalent fractional order and porosity is approximately linear when the pore distribution is almost the same. Compared with the randomly distributed pores medium, the statistical relation between equivalent fractional order and porosity of discontinuous medium with uniform distribution of different porosity shifts upward, indicating that the attenuation effect of random structure on wave is higher than that of uniform structure. This paper provides a new approach to investigate wave propagation in meso-discontinuous medium such as porous materials, rocks, shells, etc. It can be used as a basis to evaluate the dynamic response of discontinuous medium.
- fractional derivative /
- meso-discontinuous /
- wave propagation /
- finite difference method /
- equivalent fractional order

HTML全文

图 1 非连续介质微元体受力和变形的示意图

Figure 1. Schematic diagram of force and deformation of discontinuous medium

下载: 全尺寸图片幻灯片

图 2 非连续介质的非均质性

Figure 2. Heterogeneity of discontinuous medium

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图 3 不同分数阶阶数对应的波传播

Figure 3. Wave propagation with different fractional order

下载: 全尺寸图片幻灯片

图 4 细观多孔介质有限元模型及相应的波形

Figure 4. FEM of porous medium and corresponding waveform

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图 5 不同孔隙率的细观多孔介质的波传播及对应的分数阶阶数

Figure 5. Wave propagation of porous medium with different porosities and corresponding fractional order

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图 6 各孔隙率下不同孔洞分布的波形

Figure 6. Waveforms of different hole distribution under different porosity

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图 7 均匀分布的细观多孔介质的波传播及对应的分数阶阶数

Figure 7. Wave propagation of porous medium with uniformly distributed pores and corresponding fractional order

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图 8 等效分数阶阶数与细观多孔介质孔隙率之间的统计关系

Figure 8. Statistical relationship between the equivalent fractional order and the porosity of the porous medium

下载: 全尺寸图片幻灯片

图 9 材料属性对波传播的影响

Figure 9. Effect of material properties on wave propagation

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图 10 输入波脉宽对波传播的影响

Figure 10. Effect of pulse duration of input wave on wave propagation

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表 1 不同孔隙率的细观多孔介质对应的等效分数阶阶数

Table 1. Equivalent fractional order of porous medium with different porosity

编号	孔隙率/%	等效分数阶阶数	编号	孔隙率/%	等效分数阶阶数	编号	孔隙率/%	等效分数阶阶数
1	11.02	0.95	8	34.77	0.81	15	67.69	0.54
2	17.37	0.95	9	43.46	0.70	16	73.80	0.50
3	17.37	0.95	10	43.46	0.71	17	19.58	0.95
4	26.06	0.85	11	52.13	0.68	18	30.83	0.90
5	26.07	0.85	12	52.13	0.66	19	39.25	0.83
6	34.76	0.78	13	60.83	0.60	20	43.27	0.83
7	34.77	0.78	14	60.83	0.58	21	58.84	0.71

下载: 导出CSV

表 2 不同材料的物理参数

Table 2. Physical parameters of different materials

材料	密度/（kg·m⁻³）	弹性模量/GPa	波速/（m·s⁻¹）
钢	7800	210	5189
铝	2700	70	5092
铜	8960	120	3660
环氧树脂	1200	3	1581

下载: 导出CSV

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