Relationship between polyhedral structures formed by tangent planes of ellipsoidal particles and system sound velocity

doi:10.1088/1674-1056/ad7726

中国物理B ›› 2024, Vol. 33 ›› Issue (11): 118301-118301.doi: 10.1088/1674-1056/ad7726

Relationship between polyhedral structures formed by tangent planes of ellipsoidal particles and system sound velocity

Cheng-Bo Li(李成波)¹, Lin Bao(鲍琳)², and Chuang Zhao(赵闯)^2,†

1 School of Materials Science and Engineering, Anyang Institute of Technology, Anyang 455000, China;
2 College of Physics, Guizhou University, Guiyang 550025, China

收稿日期:2024-07-08 修回日期:2024-08-22 接受日期:2024-09-04 出版日期:2024-11-15 发布日期:2024-11-15
基金资助:
Supported by the National Natural Science Foundation of China (Grant Nos. 12262005, 11962003, and 11602062), the Postgraduate Education Reform and Quality Improvement Project of Henan Province (Grant No. YJS2024AL138), and the Graduate Education Reform Project of Henan Province (Grant No. 2023SJGLX096Y).

Relationship between polyhedral structures formed by tangent planes of ellipsoidal particles and system sound velocity

Cheng-Bo Li(李成波)¹, Lin Bao(鲍琳)², and Chuang Zhao(赵闯)^2,†

1 School of Materials Science and Engineering, Anyang Institute of Technology, Anyang 455000, China;
2 College of Physics, Guizhou University, Guiyang 550025, China

Received:2024-07-08 Revised:2024-08-22 Accepted:2024-09-04 Online:2024-11-15 Published:2024-11-15
Contact: Chuang Zhao E-mail:1508868030@qq.com
Supported by:
Supported by the National Natural Science Foundation of China (Grant Nos. 12262005, 11962003, and 11602062), the Postgraduate Education Reform and Quality Improvement Project of Henan Province (Grant No. YJS2024AL138), and the Graduate Education Reform Project of Henan Province (Grant No. 2023SJGLX096Y).

摘要/Abstract

摘要： Internal polyhedral structures of a granular system can be investigated using the Voronoi tessellations. This technique has gained increasing recognition in research of kinetic properties of granular flows. For systems with mono-sized spherical particles, Voronoi tessellations can be utilized, while radial Voronoi tessellations are necessary for analyzing systems with multi-sized spherical particles. However, research about polyhedral structures of non-spherical particle systems is limited. We utilize the discrete element method to simulate a system of ellipsoidal particles, defined by the equation $(\frac{x}{\alpha})^{2}+(\frac{y}{1})^{2}+(\frac{z}{1/\alpha})^{2}=1$, where $\alpha$ ranges from 1.1 to 2.0. The system is then dissected by using tangent planes at the contact points, and the geometric quantities of the resulting polyhedra in different shaped systems, such as surface area, volume, number of vertices, number of edges, and number of faces, are calculated. Meanwhile, the longitudinal and transverse wave velocities within the system are calculated with the time-of-flight method. The results demonstrate a strong correlation between the sound velocity of the system and the geometry of the dissected polyhedra. The sound velocity of the system increases with the increase in $\alpha$, peaking at $\alpha=1.3$, and then decreases as $\alpha$ continues to increase. The average volume, surface area, number of vertices, number of edges, and number of faces of the polyhedra decrease with the increase in sound velocity. That is, these quantities initially decrease with the increase in $\alpha$, reaching minima at $\alpha=1.3$, and then increase with further increase of $\alpha$. The relationship between sound velocity and the geometric quantities of the dissected polyhedra can serve as a reference for acoustic material design.

关键词: discrete element method, Voronoi tessellation, polyhedral structure, sound velocity

Abstract: Internal polyhedral structures of a granular system can be investigated using the Voronoi tessellations. This technique has gained increasing recognition in research of kinetic properties of granular flows. For systems with mono-sized spherical particles, Voronoi tessellations can be utilized, while radial Voronoi tessellations are necessary for analyzing systems with multi-sized spherical particles. However, research about polyhedral structures of non-spherical particle systems is limited. We utilize the discrete element method to simulate a system of ellipsoidal particles, defined by the equation $(\frac{x}{\alpha})^{2}+(\frac{y}{1})^{2}+(\frac{z}{1/\alpha})^{2}=1$, where $\alpha$ ranges from 1.1 to 2.0. The system is then dissected by using tangent planes at the contact points, and the geometric quantities of the resulting polyhedra in different shaped systems, such as surface area, volume, number of vertices, number of edges, and number of faces, are calculated. Meanwhile, the longitudinal and transverse wave velocities within the system are calculated with the time-of-flight method. The results demonstrate a strong correlation between the sound velocity of the system and the geometry of the dissected polyhedra. The sound velocity of the system increases with the increase in $\alpha$, peaking at $\alpha=1.3$, and then decreases as $\alpha$ continues to increase. The average volume, surface area, number of vertices, number of edges, and number of faces of the polyhedra decrease with the increase in sound velocity. That is, these quantities initially decrease with the increase in $\alpha$, reaching minima at $\alpha=1.3$, and then increase with further increase of $\alpha$. The relationship between sound velocity and the geometric quantities of the dissected polyhedra can serve as a reference for acoustic material design.

Key words: discrete element method, Voronoi tessellation, polyhedral structure, sound velocity

中图分类号: (Granular systems)

45.70.-n

46.40.Cd (Mechanical wave propagation (including diffraction, scattering, and dispersion)) 83.80.Fg (Granular solids)

Cheng-Bo Li(李成波), Lin Bao(鲍琳), and Chuang Zhao(赵闯). Relationship between polyhedral structures formed by tangent planes of ellipsoidal particles and system sound velocity[J]. 中国物理B, 2024, 33(11): 118301-118301.

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Relationship between polyhedral structures formed by tangent planes of ellipsoidal particles and system sound velocity

Relationship between polyhedral structures formed by tangent planes of ellipsoidal particles and system sound velocity

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