Chaos Solitons & Fractals最新文献

Emergence of relaxation beat-waves in genuinely nonlinear Klein-Gordon chain with bi-harmonic parametric excitation 具有双谐波参数激励的真正非线性克莱因-戈登链中弛豫节拍波的出现

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-05 DOI: 10.1016/j.chaos.2024.115692

This paper provides analytical investigation of nonstationary regimes in a strongly anharmonic Klein-Gordon chain subjected to the two-component parametric excitation. We explore the mechanisms of formation and provide a comprehensive analytical characterization of the dynamics of two distinct highly nonstationary beat-wave regimes, namely the weakly- and strongly- modulated beat-waves. To this end, we derive the double parametrically driven discrete p-Schrodinger model in the neighborhood of 2:2:1 parametric resonance. The obtained non-autonomous slow-flow model depicts the low-energy complex amplitude modulations of coupled oscillators in the vicinity of 2:2:1 resonance. Through a special coordinate transformation, we exactly reduce the slow-flow system dynamics to a beat-wave slow invariant manifold governed by three collective coordinates. To study the complex nonstationary dynamics of beat-waves, we further reduce the overall system dynamics onto the super-slow invariant manifold (SSIM) by applying an additional multi-scale procedure to the system of collective coordinates. Analysis of the system dynamics on the SSIM reveals the two types of non-stationary beat-wave regimes. The first type is a weakly modulated beat-wave response, exhibiting super-slow amplitude modulation without amplitude relaxation. The second, more intriguing type is a strongly modulated beat-wave response, which exhibits rapid amplitude relaxations characterized by two distinct behaviors: one involving rapid amplitude decay to the trivial state, and the other manifested by the recurrent relaxation oscillations. We derive analytical approximations that describe the mechanisms of formation and the entire dynamics of these highly nonstationary beat-wave states. Remarkably, the analytical model aligns satisfactorily with numerical simulations for both weakly and strongly modulated beat-wave states.

本文对受到双分量参数激励的强非谐克莱因-戈登链中的非稳态进行了分析研究。我们探讨了两种不同的高度非稳态拍波机制（即弱调制拍波和强调制拍波）的形成机制，并对其动力学特性进行了全面的分析。为此，我们推导了 2:2:1 参数共振附近的双参数驱动离散 p 薛定谔模型。得到的非自治慢流模型描述了耦合振荡器在 2:2:1 共振附近的低能复振幅调制。通过特殊的坐标变换，我们将慢流系统动力学精确还原为由三个集合坐标支配的节拍波慢不变流形。为了研究节拍波的复杂非稳态动力学，我们通过对集合坐标系应用额外的多尺度程序，进一步将整个系统动力学还原为超慢不变流形（SSIM）。对 SSIM 上系统动力学的分析揭示了两种非稳态节拍波状态。第一种是弱调制节拍波响应，表现出超慢振幅调制而无振幅松弛。第二种更有趣的类型是强调制节拍波响应，它表现出快速的振幅松弛，有两种不同的行为特征：一种是振幅快速衰减到微不足道的状态，另一种则表现为反复出现的松弛振荡。我们推导出分析近似值，描述了这些高度非稳态节拍波状态的形成机制和整个动力学过程。值得注意的是，分析模型与弱调制和强调制节拍波状态的数值模拟结果都非常吻合。

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引用次数: 0

Impulsive quasi-containment control in stochastic heterogeneous multiplex networks 随机异构多路复用网络中的脉冲准遏制控制

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-05 DOI: 10.1016/j.chaos.2024.115666

In this work, we propose a model for heterogeneous multiplex networks with stochastic perturbations. We consider multiple leaders in the networks and design an impulsive controller for cost saving to investigate the containment control problem in the stochastic heterogeneous multiplex networks. By means of the Lyapunov function method and stochastic impulsive differential equations theory, we obtain sufficient conditions in which the states of all followers converge to the bounded convex hull spanned by the states of multiple leaders. We also obtain the upper bound of the convergence region of the synchronization error system. Furthermore, we study the case with time delay and derive the sufficient conditions for the states of synchronization error to converge to the bounded region. Finally, we give two numerical examples to verify the theoretical results.

在这项工作中，我们提出了一个具有随机扰动的异构多路复用网络模型。我们考虑了网络中的多个领导者，并设计了一个用于节约成本的脉冲控制器，以研究随机异构多路复用网络中的遏制控制问题。通过 Lyapunov 函数方法和随机脉冲微分方程理论，我们得到了所有跟随者的状态收敛到多个领导者状态所跨的有界凸壳的充分条件。我们还得到了同步误差系统收敛区域的上界。此外，我们还研究了有时间延迟的情况，并推导出同步误差状态收敛到有界区域的充分条件。最后，我们给出了两个数值示例来验证理论结果。

引用次数: 0

A special memristive diode-bridge-based hyperchaotic hyperjerk autonomous circuit with three positive Lyapunov exponents 具有三个正 Lyapunov 指数的基于特殊记忆二极管桥的超混沌超杰克自治电路

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-05 DOI: 10.1016/j.chaos.2024.115704

This work presents an autonomous hyperjerk type circuit where a generalized memristor consisting of a diode-bridge and an RC filter acts as nonlinear component. The dynamics equations of the proposed circuit are presented in the form of an infinitely differentiable (i.e. smooth) system of order six. A detailed analysis of the model, carried out using classic techniques for studying nonlinear systems, reveals surprising behaviors such as the coexistence of bifurcation modes, non-trivial transient behaviors, offset boosting, torus, chaos, as well as hyperchaos with three positive Lyapunov exponents. These results are obtained by varying both the initial states and the model parameters. This multitude of dynamic properties is verified in the laboratory by carrying out series of measurements on the prototype of the memristive circuit. To the best of our knowledge, the circuit proposed in this article represents the simplest memristor-based circuit known to date in the relevant literature which can generate hyperchaotic signals with three positive Lyapunov exponents.

这项研究提出了一种自主超强型电路，其中一个由二极管桥和 RC 滤波器组成的广义忆阻器充当非线性元件。该电路的动力学方程以六阶无穷微分（即平滑）系统的形式呈现。利用研究非线性系统的经典技术对该模型进行了详细分析，发现了一些令人惊讶的行为，如分岔模式并存、非三相瞬态行为、偏移增强、环形、混沌以及具有三个正 Lyapunov 指数的超混沌。这些结果是通过改变初始状态和模型参数获得的。在实验室中，通过对忆苦思甜电路原型进行一系列测量，验证了这些动态特性的多样性。据我们所知，本文提出的电路是迄今为止相关文献中已知的最简单的基于忆阻器的电路，它可以产生具有三个正李亚普诺夫指数的超混沌信号。

引用次数: 0

A novel spatio-temporal prediction model of epidemic spread integrating cellular automata with agent-based modeling 将细胞自动机与基于代理的建模相结合的新型流行病传播时空预测模型

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-04 DOI: 10.1016/j.chaos.2024.115709

Since 2019, major infectious disease outbreaks have placed tremendous pressure on global public health systems, triggering extensive research on the predictive modeling of infectious diseases. Cellular Automaton (CA) is primarily used in the spatial prediction of infectious diseases to establish a model to for simulating the interaction between different regions and the infection risk to simulate the transmission process of the disease and predict its development trend. However, CA models are governed by initial fixed rules and local interactions, and often fail to capture the complex dynamics of epidemic transmission, which are influenced by factors such as public behavior and government intervention. In view of these limitations, we propose a factorial simulation model for the spatial spread of epidemics, the CA-ABM, which divides agents into three categories–public, government, and hospital agents–to comprehensively express the macro factors that affect the development of epidemics. Agent-Based Modeling (ABM) influences the transition rules of the CA through agent choices, constraints and supporting behaviors. Focusing on the COVID-19 pandemic in mainland China from February 6 to March 20, 2020, we simulate its spread. The results showed an average improvement of 8.4 % in prediction accuracy, with few errors, RMSE under 200, and R² values over 0.9 in most provinces, demonstrating strong macro-scale stability. This approach helps regions to understand influencing factors and enables targeted infection risk assessment and prevention. In addition, scenario analysis based on CA-ABM model changes epidemic decision-making from “prediction-response” to “scenario-response” and provides theoretical reference for future epidemic management.

2019 年以来，重大传染病的爆发给全球公共卫生系统带来了巨大压力，引发了对传染病预测建模的广泛研究。细胞自动机（Cellular Automaton，CA）主要用于传染病的空间预测，建立模拟不同区域间相互作用和感染风险的模型，模拟疾病的传播过程，预测其发展趋势。然而，CA 模型受初始固定规则和局部相互作用的制约，往往无法捕捉到受公众行为和政府干预等因素影响的流行病传播的复杂动态。鉴于这些局限性，我们提出了一种疫情空间传播的因子模拟模型--CA-ABM，将代理分为公众代理、政府代理和医院代理三类，以全面表达影响疫情发展的宏观因素。基于代理的建模（ABM）通过代理的选择、约束和支持行为来影响 CA 的过渡规则。我们以 2020 年 2 月 6 日至 3 月 20 日在中国大陆发生的 COVID-19 大流行为重点，模拟了其传播情况。结果表明，预测精度平均提高了 8.4%，误差很小，RMSE 小于 200，大多数省份的 R2 值超过 0.9，显示了较强的宏观稳定性。这种方法有助于各地区了解影响因素，从而有针对性地进行感染风险评估和预防。此外，基于 CA-ABM 模型的情景分析将疫情决策从 "预测-响应 "转变为 "情景-响应"，为未来的疫情管理提供了理论参考。

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引用次数: 0

Prescribed-time multi-coalition Nash equilibrium seeking by event-triggered communication 通过事件触发通信寻求规定时间多联盟纳什均衡

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-04 DOI: 10.1016/j.chaos.2024.115679

This article investigates the event-triggered prescribed-time Nash equilibrium seeking problem among multiple coalitions of agents in noncooperative games. Each coalition acts as a virtual player in the noncooperative game, with decisions made by its member agents. Agents lack complete information about others’ decisions and instead estimate them through a communication graph. An event-triggered prescribed-time multi-coalition Nash equilibrium seeking method is developed based on the leader-following consensus protocol, dynamic average consensus protocol, and gradient play. This method ensures the Nash equilibrium of the multi-coalition game is reached within a prescribed time, even when communication between agents only occurs under specific triggering conditions—effectively conserving communication resources. Unlike existing approaches, the proposed algorithm allows precise settling time assignment without prior knowledge of system parameters. This algorithm also prevents Zeno behavior. Lastly, the efficiency of the designed algorithm is demonstrated through simulation experiments.

本文研究了非合作博弈中多个代理联盟之间的事件触发规定时间纳什均衡寻求问题。每个联盟在非合作博弈中扮演虚拟玩家的角色，由其成员代理做出决策。代理缺乏关于他人决策的完整信息，只能通过通信图来估计。基于领导者-跟随共识协议、动态平均共识协议和梯度博弈，我们开发了一种事件触发的规定时间多联盟纳什均衡寻求方法。这种方法能确保多联盟博弈在规定时间内达到纳什均衡，即使代理之间的通信只在特定触发条件下发生，也能有效地节约通信资源。与现有方法不同的是，所提出的算法无需事先了解系统参数，即可精确分配结算时间。该算法还能防止 Zeno 行为。最后，通过模拟实验证明了所设计算法的效率。

引用次数: 0

Dynamic analysis of viscoelastic functionally graded porous beams using an improved Bernstein polynomials algorithm 使用改进伯恩斯坦多项式算法对粘弹性功能分级多孔梁进行动态分析

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-02 DOI: 10.1016/j.chaos.2024.115698

Functionally graded porous (FGP) materials have significant application potential because they can achieve many specific applications by controlling porosity and material composition. However, most current research has little emphasis on the vibration characteristics of FGP materials with viscoelastic properties. To address this issue, this article presents an improved Bernstein polynomials algorithm to establish the governing equation for analyzing the vibration response of fractional-order viscoelastic FGP beams. This method effectively resolves instability problems associated with boundary conditions. Single step Adams scheme and Newmark-β method are then utilized to solve the governing equation of the viscoelastic FGP beams. The accuracy of the proposed method is confirmed through comparison with the results obtained from the finite element method. A parametric investigation is conducted to explore the impact of porosity and its distribution pattern, power law index, boundary condition, fractional order, and viscoelasticity coefficient on the vibration characteristics of the viscoelastic FGP beams. These findings suggest that desirable dynamic properties for FGP beams can be achieved through tailoring their material gradient and porosity distribution.

功能分级多孔（FGP）材料具有巨大的应用潜力，因为它们可以通过控制孔隙率和材料成分实现许多特定应用。然而，目前大多数研究很少关注具有粘弹特性的 FGP 材料的振动特性。针对这一问题，本文提出了一种改进的伯恩斯坦多项式算法，用于建立分析分数阶粘弹性 FGP 梁振动响应的控制方程。该方法可有效解决与边界条件相关的不稳定性问题。然后利用单步 Adams 方案和 Newmark-β 方法求解粘弹性 FGP 梁的控制方程。通过与有限元法得出的结果进行比较，证实了所提方法的准确性。通过参数化研究，探讨了孔隙率及其分布模式、幂律指数、边界条件、分数阶数和粘弹性系数对粘弹性 FGP 梁振动特性的影响。这些研究结果表明，通过调整 FGP 梁的材料梯度和孔隙率分布，可以获得理想的动态特性。

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引用次数: 0

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

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

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.

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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引用次数: 0

Evaluation of human epileptic brain networks by constructing simplicial complexes 通过构建简单复合物评估人类癫痫脑网络

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-01 DOI: 10.1016/j.chaos.2024.115699

As a powerful framework, higher-order networks have gained significant attention to model the non-pairwise interactions of complex systems. Particularly, simplicial complex is an important mathematical tool which can be used to depict higher-order interactions. However, previous works on simplicial complexes have mainly focused on synthetic data. In this paper, we propose a method based on multivariate phase synchronization to construct simplicial complexes using multichannel stereo-electroencephalography (SEEG) data recorded from epilepsy patients. Furthermore, we examine its ability to describe both global and local characteristics of the higher-order brain network. Specifically, we first introduce the Hodge Laplacian to characterize higher-order interactions and employ the Euler characteristic number to determine the network synchronizability which is a significant global characteristic. Afterwards, we define an improved gravity-based centrality method to identify vital nodes in the higher-order network with simplicial complexes. Additionally, network efficiency based on the higher-order distance between different nodes is adopted to evaluate the effectiveness of this method in distinguishing the important nodes. In particular, we find that the Hippocampus and Fusiform gyrus may promote the synchronization of the epileptic brain network. All in all, we believe that our method paves the way to investigate brain networks with higher-order interactions, which contributes to identifying hubs in the epileptic network and has potential applications in epileptic treatment.

作为一个强大的框架，高阶网络在模拟复杂系统的非成对相互作用方面受到了广泛关注。其中，简单复合物是一种重要的数学工具，可用于描述高阶相互作用。然而，以往关于简单复数的研究主要集中在合成数据上。在本文中，我们提出了一种基于多变量相位同步的方法，利用癫痫患者记录的多通道立体脑电图（SEEG）数据构建简单复合物。此外，我们还研究了该方法描述高阶大脑网络的全局和局部特征的能力。具体来说，我们首先引入霍奇拉普拉斯来描述高阶相互作用的特征，并利用欧拉特征数来确定网络同步性，这是一个重要的全局特征。然后，我们定义了一种改进的基于引力的中心性方法，以简约复数识别高阶网络中的重要节点。此外，我们还采用了基于不同节点间高阶距离的网络效率来评估该方法在区分重要节点方面的有效性。我们特别发现海马回和镰状回可能会促进癫痫脑网络的同步化。总之，我们认为我们的方法为研究具有高阶交互作用的大脑网络铺平了道路，有助于识别癫痫网络中的枢纽，并在癫痫治疗中具有潜在的应用价值。

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引用次数: 0

Dynamical analysis and event-triggered neural backstepping control of two Duffing-type MEMS gyros with state constraints 带状态约束的两个 Duffing 型 MEMS 陀螺的动态分析和事件触发神经反步控制

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-01 DOI: 10.1016/j.chaos.2024.115691

The DSP (Digital Signal Processing) implementation of two Duffing-type micro-electro-mechanical systems (MEMS) gyros and their event-triggered neural backstepping control with state constraints are investigated in this paper. Initially, we design the two Duffing-type MEMS gyros with a fully decoupled structure and establish a mathematical model based on the Newton's Second Law and the Lagrange equation. Due to the significant differences in the integrated circuit design and engineering application between embedded platforms and computer simulations, we selected the DSP platform to better characterize two Duffing-type MEMS gyros. Based on this, we explore nonlinear dynamic behaviors through phase and time history diagrams from the DSP platform as well as Lyapunov exponents under different coupling and damping coefficients, thereby identifying the existence of harmful chaotic phenomena in such gyros. Subsequently, to address chaotic oscillations along with overcoming the troubles of state constraints, uncertain disturbances and communication burden in the system, we incorporate the integral barrier Lyapunov function (IBLF) to limit the position of the proof mass within the physical limit. Furthermore, a type-2 sequential fuzzy neural network (T2SFNN) is used to approximate unknown nonlinear terms and the switching threshold event-triggered (STET) mechanism is utilized to save communication bandwidth. Then, an event-triggered neural backstepping controller is proposed to successfully achieve safety, high-precision and low resource consumption control of such gyros, ensuring that all signals in the closed-loop system remain bounded. Finally, simulation results and comparative experiments demonstrate the effectiveness and superiority of our proposed control scheme.

本文研究了两个 Duffing 型微机电系统（MEMS）陀螺仪的 DSP（数字信号处理）实现及其带状态约束的事件触发神经反步进控制。首先，我们设计了两个完全解耦结构的达芬奇型微机电系统陀螺仪，并建立了基于牛顿第二定律和拉格朗日方程的数学模型。由于嵌入式平台和计算机仿真在集成电路设计和工程应用方面存在显著差异，我们选择了 DSP 平台来更好地表征两个 Duffing 型 MEMS 陀螺。在此基础上，我们通过 DSP 平台的相位图和时间历程图以及不同耦合系数和阻尼系数下的 Lyapunov 指数来探索非线性动态行为，从而确定此类陀螺仪中是否存在有害的混沌现象。随后，为了解决混沌振荡问题，同时克服系统中的状态约束、不确定干扰和通信负担等问题，我们加入了积分屏障 Lyapunov 函数（IBLF），将证明质量的位置限制在物理极限内。此外，我们还使用了 2 型序列模糊神经网络（T2SFNN）来逼近未知的非线性项，并利用开关阈值事件触发（STET）机制来节省通信带宽。然后，提出了一种事件触发神经反步进控制器，以成功实现对此类陀螺仪的安全、高精度和低资源消耗控制，并确保闭环系统中的所有信号保持有界。最后，仿真结果和对比实验证明了我们提出的控制方案的有效性和优越性。

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引用次数: 0

Relationship between micro-pores fractal characteristics about NMR T2 spectra and macro cracks fractal laws based on box dimension method of coal under impact load from energy dissipation theory 基于能量耗散理论的冲击载荷下煤炭箱形尺寸法的核磁共振 T2 光谱微孔分形特征与宏观裂缝分形规律之间的关系

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2024-11-01 DOI: 10.1016/j.chaos.2024.115685

The development and utilization of deep formation resources are easily disrupted by impact loads. To investigate what effect of impact on the pore structure and energy evolution of coal, the dynamic compression tests were performed by using the Split Hopkinson Pressure Bar (SHPB) test system. The fractal characteristics of macro cracks were analyzed by box dimension, the micro-pores structure and fractal features of coal samples were studied about nuclear magnetic resonance (NMR), which clarified the intrinsic relationship between fracture structure characteristics and energy dissipation. The results showed that with increasing impact velocity from 1.27 m/s to 4.90 m/s, the dynamic strength and peak strain increased by 85.11 % and 53.76 %, respectively. The fractal dimension of the cracks grew by 26.87 %, and the fractal dimension of pore network and full aperture decreases gradually. With increasing impact velocity, the fracture dissipation energy and energy dissipation rate of coal samples increase exponentially. As the energy dissipation rate increases, the cracks fractal increases in a quadratic function relationship and the pores fractal decreases continuously. Low-velocity impacts induce dislocation plugging between coal matrix crystals, while impact effect causes more dislocations to form stress concentrations at pore tips. When the energy accumulation reaches its maximum value, the content of mesopores and macropores together with the pore connectivity increases. Instantaneous disturbance creates more macroscopic fracture surfaces in the coal, resulting in large-scale fracture instability. This research findings will provide some theoretical foundations to understand the formation mechanism of dynamic disasters in deep mines.

深部地层资源的开发和利用很容易受到冲击载荷的干扰。为了研究冲击载荷对煤炭孔隙结构和能量演化的影响，利用分体式霍普金森压力棒（SHPB）试验系统进行了动态压缩试验。通过箱形尺寸分析了宏观裂缝的分形特征，并利用核磁共振（NMR）研究了煤样的微孔结构和分形特征，从而明确了断裂结构特征与能量耗散之间的内在联系。结果表明，随着冲击速度从 1.27 m/s 增加到 4.90 m/s，动态强度和峰值应变分别增加了 85.11 % 和 53.76 %。裂缝的分形维数增加了 26.87%，孔隙网络和全孔径的分形维数逐渐减小。随着冲击速度的增加，煤样的断裂耗能和耗能率呈指数增长。随着耗能率的增加，裂缝分形呈二次函数关系增加，孔隙分形不断减小。低速冲击会引起煤基体晶体间的位错堵塞，而冲击效应会使更多的位错在孔隙尖端形成应力集中。当能量积累达到最大值时，中孔和大孔的含量以及孔隙连通性都会增加。瞬时扰动在煤中形成更多的宏观断裂面，导致大尺度断裂不稳定性。这一研究成果将为理解深部矿井动态灾害的形成机理提供一些理论基础。

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引用次数: 0