Construction of a deterministic mathematical model for the spatial-mass distribution of random fragments produced by cased charge explosion

IF 5.3 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Chaos Solitons & Fractals Pub Date : 2024-11-02 DOI:10.1016/j.chaos.2024.115703
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Abstract

To evaluate the destructive effects of fragment impacts on structures or personnel, it is crucial to assess the velocity, mass, size, and impact location of the fragments, as well as establish the correlation between these factors. This paper presents the experimental measurement of fragment velocities produced by the explosion of a cased charge, the fragments resulting from the explosion are collected and steel plates are used to record the impact locations and sizes of the fragments. Based on the experimental results, the calculation models of fragment velocity, fragment mass distribution and fragment scattering angle are corrected, the spatial distribution models of fragment size and number are established, and the functional relationship between fragment mass and size is constructed. Given the aforementioned research findings, the fragment spatial-mass distribution models based on the size distribution function and based on the mass distribution function are constructed, and the fragment space-mass distributions corresponding to the number of impact regions of 1, 5 and 10 are analyzed, and the effect of the number of impact location divisions on the fragment space-mass distribution is explored. The research results show that, for the current test charge, the fragment spatial-mass distribution model based on the size distribution function aligns most accurately with experimental results when the impact regions is divided into 10. The number of impact locations designated within each region is directly proportional to the number of fragments in that specific region. Notably, the impact location of the largest fragment occurs at 0.8 times the length of the impact region, whereas the peak fragment impact density occurs at 0.743 times the length of the impact region. The spatial-mass distribution model proposed in this paper successfully correlates the velocity, mass, size and impact location of the fragments, providing a realistic theoretical representation of the spatial geometric distribution of the fragments.
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构建套管炸药爆炸产生的随机碎片空间质量分布的确定性数学模型
要评估碎片撞击对结构或人员的破坏性影响,关键是要评估碎片的速度、质量、大小和撞击位置,并建立这些因素之间的相关性。本文介绍了对套管装药爆炸产生的碎片速度的实验测量,收集了爆炸产生的碎片,并用钢板记录了碎片的撞击位置和大小。根据实验结果,修正了碎片速度、碎片质量分布和碎片散射角的计算模型,建立了碎片大小和数量的空间分布模型,并构建了碎片质量和大小之间的函数关系。根据上述研究成果,构建了基于尺寸分布函数和基于质量分布函数的碎片空间-质量分布模型,分析了撞击区域数量为 1、5 和 10 时对应的碎片空间-质量分布,探讨了撞击位置划分数量对碎片空间-质量分布的影响。研究结果表明,对于当前的试验装药,当撞击区域划分为 10 个时,基于尺寸分布函数的碎片空间-质量分布模型与实验结果的吻合度最高。每个区域内指定的撞击位置数量与该特定区域内的碎片数量成正比。值得注意的是,最大碎片的撞击位置出现在撞击区域长度的 0.8 倍处,而碎片撞击密度峰值出现在撞击区域长度的 0.743 倍处。本文提出的空间-质量分布模型成功地将碎片的速度、质量、大小和撞击位置联系起来,从理论上真实地再现了碎片的空间几何分布。
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来源期刊
Chaos Solitons & Fractals
Chaos Solitons & Fractals 物理-数学跨学科应用
CiteScore
13.20
自引率
10.30%
发文量
1087
审稿时长
9 months
期刊介绍: Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.
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