Applied Mathematical Modelling最新文献_第6页

Aeroelasticity of membrane airfoils and flexible-chord airfoils with permeable trailing sections

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-15 DOI: 10.1016/j.apm.2025.115947

Omar S. Hussein

This work addresses the aeroelasticity of airfoils with permeable trailing sections which is a topic that has not been studied in the literature before. There has been an increasing interest in the past few years regarding the analysis of permeable airfoils from the aerodynamics and aeroacoustics points of view. So, this work adds a new aspect to the analysis by considering the airfoil elasticity and flexibility effect. Two types of airfoils are considered: membrane airfoils and flexible-chord airfoils. Both static and dynamic aeroelastic studies of permeable airfoils are presented through a parametric analysis to investigate the effects of the permeable section length, permeability factor, boundary conditions represented by the membrane fixed or elastic supports and the elastic center position of flexible-chord airfoils, and the elastic properties of the airfoils like the bending rigidity of flexible-chord airfoils and the tension coefficient of membrane airfoils. The aeroelastic model of permeable airfoils is derived using the Hamilton's variational principle and the finite element method. The finite element system of equations is presented in a time domain nonlinear form to account for the nonlinear stiffening of membrane airfoils. The seepage flow through the permeable section is modeled using Darcy's law. The effects of permeability on the static aerodynamic coefficients, the dynamic response under a sinusoidal gust, and the aeroelastic instabilities (divergence and flutter) are investigated. The study aims at the aeroelastic performance of permeable airfoils subjected to incompressible airflows at small angles of attack and moderate to high Reynolds numbers, so the potential flow theory is adopted for the aerodynamic modeling. The analysis shows that permeability can have a significant effect on the aeroelastic responses of airfoils. The trailing permeable section changes the pressure distribution which changes the lift curve slope and the aerodynamic center position which in turn affects the aeroelastic instabilities and responses. This permeability effect strongly depends on the airfoil's stiffness represented by the bending rigidity of the flexible-chord airfoils and the tension in the membrane airfoils.

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引用次数: 0

Vibration analysis of non-homogenous single-link flexible manipulator in uncertain environment

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-14 DOI: 10.1016/j.apm.2025.115939

Priya Rao , Dhabaleswar Mohapatra , S. Chakraverty , Debanik Roy

This paper presents a novel dynamic model of a dual-cable-strapped single-link flexible manipulator under an uncertain workspace. The material of the link of the manipulator is considered to be non-homogeneous with inherent non-linearity, which is crucial in modelling. In this regard, linear and quadratic variations in the density of the material of the flexible link with space coordinates are considered. Uncertainty is introduced into its parameters in order to make the real-time dynamics of the flexible manipulator more challenging. Fuzzy parameters, in support of uncertainty, are invoked in the spring constants of the cables for modelling using Triangular Fuzzy Numbers (TFN). In particular, Interval Type-2 Triangular Fuzzy Numbers (IT2TFN) are considered in this investigation since higher-order fuzzy numbers can be beneficial, as the presence of uncertainty in the membership grade may also be unavoidable. The non-homogeneous flexible link is modelled as an Euler-Bernoulli beam, and the non-linear equations of motion are derived using Hamilton's principle and two boundary conditions. It may be difficult to obtain the exact solution of the governing differential equation because of the non-homogeneity in the parameters associated with the link. In this regard, the Adomian Decomposition Method (ADM) is implemented in the crisp as well as uncertain scenario to determine the natural frequencies of the single-link flexible manipulator. The existence and uniqueness of the solution is also illustrated. Tabular and graphical results are presented for validation and better visualisation.

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引用次数: 0

Data-driven modeling for rapid prediction of aerodynamic noise directivity of flow over a cylinder 基于数据驱动的汽缸流动气动噪声指向性快速预测模型

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-14 DOI: 10.1016/j.apm.2025.115937

Yao Jin , Fei Liao , Jinsheng Cai

Conventional high-fidelity simulations are prohibitively expensive for aerodynamic noise optimization and control applications. Developing surrogate models of minimal computational costs provide efficient alternatives in noise estimation for various numerical conditions. In the present work, three data-driven acoustic directivity modeling strategies are proposed, including a purely data-driven POD model and two semi-analytical data-driven models: force-model and dipole-model. All the three models significantly accelerate the prediction of noise directivity, which is attributed to their independence of conventional numerical approaches, despite with minor discrepancies in accuracy among each other. The POD-model is constructed based on the singular vector decomposition and an interpolation method, enabling high accuracy but requiring a large amount of training data. A sensitivity study is conducted on four parametric aspects, such as mode number, interpolation method, inherent flow nonlinearity in wake region, and the distribution of interpolation states in training datasets. The force-model, derived from the Ffowcs Williams-Hawkings equation, requires force fluctuations on the body surfaces. Also the dipole-model, leveraging the analytical formulation of dipole velocity potential, requires a careful specification of potential coefficient. These required information in force-model and dipole-model are directly approximated by data regression methods. Compared to POD-model, the notable merit of force-model and dipole-model is that rapid predictions can be implemented with reduced data requirements.

传统的高保真仿真对于气动噪声优化和控制应用来说是非常昂贵的。开发计算成本最小的替代模型为各种数值条件下的噪声估计提供了有效的替代方法。本文提出了三种数据驱动的声指向性建模策略，包括纯数据驱动的POD模型和两种半解析数据驱动模型：力模型和偶极子模型。这三种模型都显著地加速了噪声指向性的预测，这归因于它们与传统数值方法的独立性，尽管它们之间的精度存在微小差异。该pod模型基于奇异向量分解和插值方法构建，精度高，但需要大量的训练数据。从模态数、插补方法、尾迹区固有流动非线性、插补状态在训练数据集中的分布等四个参数方面进行灵敏度研究。从Ffowcs williams - hawkins方程推导出的力模型要求物体表面的力波动。此外，利用偶极速度势的解析公式的偶极模型需要仔细地说明势系数。力模型和偶极子模型所需要的这些信息通过数据回归方法直接逼近。与pod模型相比，力模型和偶极子模型的显著优点是可以在较少的数据要求下实现快速预测。

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引用次数: 0

Phase-field simulation for the mechanical and fracture properties of NdFeB under quasi-static loading conditions

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-14 DOI: 10.1016/j.apm.2025.115944

Xinyu Zheng, Liqun Wang, Guolai Yang, Jianli Ge

NdFeB has been widely used in various fields due to its excellent magnetic properties. However, as a brittle material, its mechanical properties limit its application, and research into these properties remains inadequate. This study employs the phase field method to investigate the mechanical response and fracture mechanism of NdFeB. The phase field method, a numerical approach that has garnered significant attention in recent years, is a highly effective crack regularization variational method for simulating crack initiation and propagation. A phase field model for the fracture surface of NdFeB was established, with the software implementation method provided. The accuracy of the model was validated through comparisons with several typical experimental results. Finally, an analysis was conducted on the impact of structural dimensions, positional tolerances, and pre-existing cracks on the mechanical properties of NdFeB specimens, with a detailed examination of the crack propagation process.

引用次数: 0

Mathematical modelling for large-aperture mirror systems: enabling optical-mechanical performance analysis and support structure optimization 大口径反射镜系统的数学建模：实现光学机械性能分析和支撑结构优化

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-13 DOI: 10.1016/j.apm.2025.115938

Pengwei Liang , Xueguan Song , Yong Xiang , Zhaoyang Li , Tao Zhang , Junwei Zhang

Large-aperture mirror systems (LAMS) are widely used in fields such as electro-optical countermeasures, spaceborne remote sensing, and laser communication. Accurate modeling and analysis of LAMS are crucial for its design and optimization. To transition from one-off simulation models to a generalized theoretical mathematical model, this paper presents a theoretical modeling method that combines the Reciprocal Theorem of Work and the Perturbation Method. First, based on the Kirchhoff plate theory, a variable-coefficient deflection governing equations for LAMS is derived. Then, using the principles of the Perturbation Method, an analytical solution for the governing equations within the framework of the Reciprocal Theorem of Work is obtained. Additionally, the proposed governing equations are validated for convergence, and it is found that the solution converges when m ≥ 3. By comparing with FEM results, the accuracy of the proposed model is confirmed, with the root mean square error (RMSE) below 9.918 × 10^-4 and R² exceeding 0.875. Furthermore, the influence of higher-order perturbation terms and computational efficiency are analyzed. The results show that the first-order perturbation solution satisfies the accuracy requirements, and the proposed method offers significant computational efficiency advantages over FEM. Finally, for a specific LAMS model, the proposed governing equations are applied to optimize its support scheme. The results indicate that, for 9 support points, the optimal radius of the inner supports is 0.267a, while the outer supports have an optimal radius of 0.775a. For 18 support points, the optimal radius of the inner supports is 0.343a, with the outer supports having an optimal radius of 0.811a. Overall, the proposed method establishes a theoretical foundation for designing and optimizing the support structures of LAMS, significantly facilitating engineers in optimizing its optomechanical performance.

大口径反射镜系统在光电对抗、星载遥感、激光通信等领域有着广泛的应用。准确的建模和分析对其设计和优化至关重要。为了从一次性的仿真模型过渡到广义的理论数学模型，本文提出了一种结合功的互反定理和摄动法的理论建模方法。首先，基于Kirchhoff板理论，推导了LAMS变系数挠度控制方程。然后，利用摄动法的原理，在功的互反定理的框架内得到了控制方程的解析解。此外，对所提出的控制方程进行了收敛性验证，发现当m≥3时，解是收敛的。通过与有限元结果的比较，验证了所建模型的准确性，均方根误差（RMSE）小于9.918 × 10-4， R2大于0.875。进一步分析了高阶扰动项和计算效率的影响。结果表明，一阶摄动解满足精度要求，与有限元方法相比，该方法具有显著的计算效率优势。最后，针对一个具体的LAMS模型，应用所提出的控制方程对其支撑方案进行优化。结果表明：对于9个支撑点，内支架的最优半径为0.267a，外支架的最优半径为0.775a。对于18个支撑点，内支撑点的最佳半径为0.334 a，外支撑点的最佳半径为0.811a。总体而言，所提出的方法为LAMS支撑结构的设计和优化奠定了理论基础，为工程师优化其光力学性能提供了显著的便利。

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引用次数: 0

Random walk models of advection-diffusion in layered media 分层介质中平流扩散的随机游走模型

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-13 DOI: 10.1016/j.apm.2025.115942

Elliot J. Carr

Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such transport processes are well established, they fail to account for randomness inherent in many problems and are valid only for a large number of particles. To address this, this paper derives a suite of equivalent random walk (discrete-time discrete-space) models for several standard continuum (partial differential equation) models of diffusion and advection-diffusion across a fully- or semi-permeable interface. Our approach involves discretising the continuum model in space and time to yield a Markov chain, which governs the transition probabilities between spatial lattice sites during each time step. Discretisation in space is carried out using a standard finite volume method while two options are considered for discretisation in time. A simple forward Euler discretisation yields a local (nearest-neighbour) random walk with simple analytical expressions for the transition probabilities while an exact exponential discretisation yields a non-local random walk with transition probabilities defined numerically via a matrix exponential. Constraints on the size of the spatial and/or temporal steps are provided for each option to ensure the transition probabilities are in

[0, 1]

. MATLAB code comparing the random walk and continuum models is available on GitHub (https://github.com/elliotcarr/Carr2024c) with simulation results demonstrating good agreement for several example problems.

非均质层状介质中粒子的扩散和对流输运的数学建模对于计算、生物和医学物理学中的许多应用都是重要的。虽然这种输运过程的确定性连续体模型已经很好地建立起来，但它们无法解释许多问题中固有的随机性，并且仅对大量粒子有效。为了解决这个问题，本文导出了一套等效的随机游走（离散时间-离散空间）模型，用于几个标准的连续介质（偏微分方程）扩散和平流扩散在全渗透或半渗透界面上的模型。我们的方法包括在空间和时间上离散连续体模型以产生马尔可夫链，该链控制每个时间步长期间空间点阵点之间的转移概率。在空间上采用标准有限体积法进行离散，在时间上考虑两种离散方法。简单的前向欧拉离散化产生具有简单过渡概率解析表达式的局部（最近邻）随机游走，而精确的指数离散化产生具有通过矩阵指数数值定义的过渡概率的非局部随机游走。为每个选项提供了对空间和/或时间步骤大小的约束，以确保过渡概率在[0,1]内。比较随机漫步和连续模型的MATLAB代码可在GitHub （https://github.com/elliotcarr/Carr2024c）上获得，仿真结果表明几个示例问题的一致性很好。

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引用次数: 0

Modeling of CNT alignment state on the strain sensing characteristics of MWCNT-based nanocomposites 碳纳米管对准状态对mwcnts基纳米复合材料应变传感特性的影响

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-13 DOI: 10.1016/j.apm.2025.115946

Xiaodong Xia , Junhua Xiao , Weidong Yang , George J. Weng

The strain sensing characteristics of MWCNT-based nanocomposite sensors are highly dependent on the orientation and distribution of CNTs. Most CNT sensors are neither perfectly aligned nor randomly oriented; they are just the two limiting state of partially aligned sensors. To cover this wider distribution, an anisotropic homogenization model is established to study the axial and transverse multi-field coupled performances of MWCNT-based nanocomposite strain sensors from perfectly aligned to randomly oriented state. The transversely isotropic conductivity and mechanical moduli are utilized as the dual homogenization parameters in the present anisotropic analysis. The effective mechanical moduli are evaluated via the Mori-Tanaka method, while the electrical conductivities are calculated by the effective-medium approximation. The loading-dependent tunneling distance among the partially aligned MWCNTs is established under the axial or transverse loading to assess the contribution of electron tunneling. The predicted axial and transverse strain sensing capacities, including the resistance change ratios and strain sensitivity factors, of partially aligned MWCNT-based nanocomposite sensors are demonstrated and shown to agree with experiments. The axial sensing characteristics of a partially aligned strain sensor is higher than that of a randomly oriented one due to the alignment of MWCNTs. The optimal MWCNT volume fraction of high strain sensing characteristics is determined to be near the percolation threshold. The revealed anisotropic electromechanically coupled behaviors can provide guidance to tailor the axial and transverse sensing characteristics for the general class of partially aligned nanocomposite strain sensors.

基于mwcnts的纳米复合材料传感器的应变传感特性高度依赖于CNTs的取向和分布。大多数碳纳米管传感器既不完全对齐也不随机定向；它们只是部分对准传感器的两种极限状态。为了覆盖这一更广泛的分布，建立了各向异性均匀化模型，研究了基于mwcnt的纳米复合材料应变传感器从完美排列到随机取向状态下的轴向和横向多场耦合性能。在本各向异性分析中，横向各向同性电导率和力学模量作为双均质参数。有效力学模量采用Mori-Tanaka法计算，电导率采用有效介质近似法计算。在轴向或横向加载下，建立了部分排列的MWCNTs之间与负载相关的隧穿距离，以评估电子隧穿的贡献。对部分对准mwcnt纳米复合材料传感器的轴向和横向应变传感能力（包括电阻变化率和应变敏感系数）进行了验证，并与实验结果相吻合。由于MWCNTs的对准，部分对准应变传感器的轴向传感特性比随机取向应变传感器的轴向传感特性更高。确定了具有高应变传感特性的最佳MWCNT体积分数接近渗透阈值。所揭示的各向异性机电耦合行为可以为定制一般类型的部分对准纳米复合应变传感器的轴向和横向传感特性提供指导。

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引用次数: 0

Multivariate grey prediction model with fractional time-lag parameter and its application

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-11 DOI: 10.1016/j.apm.2025.115940

Bo Zeng, Yibo Tuo

The time-lag parameter captures the asynchronous relationship between dependent and independent variables. However, traditional time-lag parameters have two limitations: they are restricted to positive integers, and their identification relies on subjective methods, reducing model adaptability and performance. To address these issues, a new multivariate grey prediction model, NSGM(1,N,τ), is proposed. Built upon the classic NSGM(1,N) framework, the proposed model incorporates the cubic spline interpolation method to extend the time-lag parameter from positive integers to fractions, effectively eliminating the aforementioned limitations. Applied to simulate and predict Jiangsu Province's port cargo throughput (PCT), the NSGM(1,N,τ) model achieved a mean absolute percentage error (MAPE) of just 0.7382 %, outperforming two similar models with MAPEs of 7.5897 % and 1.3097 %. This advancement enhances the predictive capabilities of the multivariate grey prediction model and offers a robust method for forecasting PCT with high precision.

引用次数: 0

A thermodynamic constitutive model based on uncoupled physical mechanisms for polymer-based shape memory composites and its application in 4D printing 基于非耦合物理机制的聚合物形状记忆复合材料热力学本构模型及其在4D打印中的应用

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-11 DOI: 10.1016/j.apm.2025.115926

Hao Duan , Jianping Gu , Huiyu Sun , Hao Zeng , Jesus A. Rodriguez-Morales

Four-dimensional (4D) printing is a new interdisciplinary research field that integrates sophisticated manufacturing, smart materials and mechanics. Shape memory polymer (SMP) and their composites (SMPCs) have been widely used in the field of 4D printing due to their smart and rapid response. Thus, we develop a novel thermodynamic constitutive model for SMP and SMPC, and investigate its application in 4D printing. Structure relaxation and stress relaxation are considered to follow different physical mechanisms but are related by an internal thermodynamic state variable that can represent the non-equilibrium structure. Founded on the thermodynamic variable, a physics-based fictive temperature theory is constructed for structure relaxation, and also a new stress relaxation model is proposed to characterize the time-dependent behaviors related to mechanical changes. It is shown that the influences of temperatures, strain rates, pre-strains, reinforcing fillers, and recovery conditions on stress-strain and shape memory responses are well predicted by the thermodynamic constitutive model.

四维（4D）打印是一个新的跨学科研究领域，集精密制造、智能材料和力学于一体。形状记忆聚合物（SMP）及其复合材料（smpc）因其智能、快速的响应特性在4D打印领域得到了广泛的应用。因此，我们建立了一种新的SMP和SMPC的热力学本构模型，并研究了其在4D打印中的应用。结构松弛和应力松弛被认为遵循不同的物理机制，但由一个可以表示非平衡结构的内部热力学状态变量联系在一起。在热力学变量的基础上，建立了基于物理的结构松弛理论，并提出了一种新的应力松弛模型来表征与力学变化相关的随时间行为。结果表明，温度、应变速率、预应变、补强填料和恢复条件对应力-应变和形状记忆响应的影响可以用热力学本构模型很好地预测。

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引用次数: 0

Innovative data-driven algorithm for defect parameter identification in large-scale structures 大型结构缺陷参数识别的创新数据驱动算法

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-10 DOI: 10.1016/j.apm.2025.115935

Shouyan Jiang , Wangtao Deng , Peng Zhang , Guofu Hu , Chengbin Du

This study proposes an innovative data-driven algorithm that combines the scaled boundary finite element method with an autoencoder and a causal dilated convolutional neural network for defect identification in large-scale structures. The scaled boundary finite element method simulates the propagation of waves in large-scale structures containing various types of defects. Conveniently, the scaled boundary finite element method can simulate different types of defects within structures and, by discretizing only the boundaries of structures, efficiently generate sufficient training data. To simulate wave propagation in large-scale structures, an absorbing boundary model based on Rayleigh damping is established, avoiding computations across the entire structural domain. The affinity propagation clustering algorithm is employed to optimize the number and layout of sensors, and the optimized multi-sensor data serve as the original training samples for autoencoder feature extraction. Autoencoder exhibits strong nonlinear feature extraction capabilities, mapping the high-dimensional original input feature vector space to a low-dimensional latent feature vector space to obtain low-dimensional latent features for network model training. This effectively improves the learning efficiency of the network model. The constructed causal dilated convolutional neural network model ensures orderliness of temporal data and achieves a larger receptive field without increasing neural network complexity, thereby capturing more historical information. Numerical examples demonstrate that the proposed model can accurately identify the quantified information of defects in large-scale structures. Compared with the previous model, the proposed model exhibits improved robustness.

本研究提出了一种创新的数据驱动算法，该算法将尺度边界有限元法与自编码器和因果扩展卷积神经网络相结合，用于大规模结构的缺陷识别。尺度边界有限元法模拟了波在含多种缺陷的大尺度结构中的传播。比例边界有限元法可以方便地模拟结构内部不同类型的缺陷，并且只对结构的边界进行离散化，可以有效地生成足够的训练数据。为了模拟波在大尺度结构中的传播，建立了基于瑞利阻尼的吸收边界模型，避免了整个结构域的计算。采用亲和传播聚类算法对传感器数量和布局进行优化，优化后的多传感器数据作为自编码器特征提取的原始训练样本。Autoencoder具有较强的非线性特征提取能力，将高维原始输入特征向量空间映射到低维潜在特征向量空间，获得用于网络模型训练的低维潜在特征。这有效地提高了网络模型的学习效率。所构建的因果扩展卷积神经网络模型保证了时间数据的有序性，在不增加神经网络复杂性的情况下实现了更大的接受场，从而捕获了更多的历史信息。数值算例表明，该模型能准确识别大尺度结构中缺陷的量化信息。与之前的模型相比，该模型具有更好的鲁棒性。

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引用次数: 0