Applied Mathematical Modelling最新文献_第7页

A new variational integrator for constrained mechanical system dynamics 用于约束机械系统动力学的新型变分积分器

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2024-09-23 DOI: 10.1016/j.apm.2024.115719

A new variational integrator is proposed to solve constrained mechanical systems. The main distinguishing feature of the present integrator comes from the distinct discretization of Lagrangians based on the Hamilton's principle in its most general form. Specifically, Hermite interpolation is used for discrete positions, which provides at least

C^{1}

continuity for generalized coordinates. The velocities and momentums are interpolated using quadratic polynomials for the consistency, such that the kinematic relation between velocities and positions can be exactly satisfied. Meanwhile, the Gauss-Legendre quadrature rule is employed to guarantee the accuracy of discrete Lagrange equations. To tackle constrained mechanical systems, a coordinate partition approach is used to eliminate the constraint equations. The local incremental rotation vector is exploited to get rid of rotation singularities in spatial problems. Moreover, an adaptive stepsize strategy is implemented to improve the efficiency. The strengths of the new integrator lie in the accessible large step sizes in the simulation and its global second-order accuracy for positions as well as velocities. Several examples are performed and analyzed to validate its accuracy and capabilities.

本文提出了一种新的变分积分器，用于求解约束机械系统。本积分器的主要特点来自基于汉密尔顿原理最一般形式的拉格朗日离散化。具体来说，离散位置采用 Hermite 插值法，这为广义坐标提供了至少 C1 的连续性。速度和动量采用二次多项式插值，以保证一致性，从而使速度和位置之间的运动学关系得到精确满足。同时，采用高斯-列根德正交法则来保证离散拉格朗日方程的精度。针对受约束的机械系统，采用坐标分割法消除约束方程。利用局部增量旋转向量来消除空间问题中的旋转奇异性。此外，还采用了自适应步长策略来提高效率。新积分器的优势在于可以在模拟中使用较大的步长，以及对位置和速度的全局二阶精度。为了验证其精度和能力，我们对几个实例进行了分析。

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引用次数: 0

Thermoelastic damping properties in hemi-ellipsoidal shells with variable thickness 厚度可变半椭圆形壳体的热弹性阻尼特性

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2024-09-22 DOI: 10.1016/j.apm.2024.115720

Thermoelastic damping (TED) is a fundamental dissipation mechanism that inevitably exists in shell resonators with high quality factors. Based on the thermal energy method, this paper demonstrates an effective method for the TED characterization of the hemi-ellipsoidal shells with variable thickness which manifest lower TED compared with the hemispherical shells. The equation of motion of the hemi-ellipsoidal shell under clamped-free boundary conditions is established by Hamilton's principle and the assumed mode method, and the natural frequencies and mode shape functions of the hemi-ellipsoidal shell with variable thickness are obtained by solving the eigenvalue problem. The temperature field is acquired by solving the heat conduction equation along the radial direction, and an analytical model for the TED of the hemi-ellipsoidal shell with variable thickness is presented by calculating the maximum elastic potential energy and the work lost per cycle of vibration due to irreversible heat conduction. Analysis on TED at the vibration patterns of meridional wave number m = 1 and the circumferential wave number n = 2 or 3 where the shell resonators typically operate is carried out. The analytically calculated TED results are compared with those of the finite element method (FEM) to verify the feasibility and correctness of the present method. The influences of the geometrical parameters on the TED characteristics of the hemi-ellipsoidal shells with variable thickness are analyzed in detail. A meaningful discovery is that compared with the hemispherical shell, the hemi-ellipsoidal shell with variable thickness has a smaller TED when its semiminor axis is shorter than the semimajor axis, which is particularly significant for optimizing the design of the shell resonators with high quality factors.

热弹性阻尼（TED）是一种基本的耗散机制，不可避免地存在于具有高品质因数的壳谐振器中。与半球形壳体相比，厚度可变的半椭圆形壳体表现出更低的 TED，本文基于热能法，展示了一种有效的 TED 表征方法。通过汉密尔顿原理和假定模态法建立了无夹紧边界条件下半椭圆形壳的运动方程，并通过求解特征值问题得到了厚度可变的半椭圆形壳的固有频率和模态振型函数。通过求解沿径向的热传导方程获得温度场，并通过计算不可逆热传导导致的最大弹性势能和每个振动周期的功损失，提出了厚度可变的半椭圆形壳体的 TED 分析模型。在壳体谐振器通常工作的经向波数 m = 1 和周向波数 n = 2 或 3 的振动模式下，对 TED 进行了分析。分析计算的 TED 结果与有限元法（FEM）的结果进行了比较，以验证本方法的可行性和正确性。详细分析了几何参数对厚度可变的半椭圆形壳的 TED 特性的影响。一个有意义的发现是，与半球形壳相比，厚度可变的半椭圆形壳的半主轴短于半长轴时，其 TED 更小，这对于优化设计具有高品质因数的壳谐振器尤为重要。

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引用次数: 0

Low-velocity impact response of sandwich plates with corrugation star-shaped honeycomb hybrid core 带波纹星形蜂窝混合芯材的夹层板的低速冲击响应

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2024-09-21 DOI: 10.1016/j.apm.2024.115715

Compared with traditional lightweight corrugation and honeycomb cores, the novel cellular structure exhibiting a negative Poisson's ratio possesses distinctive mechanical deformation features, making it suitable for modeling lightweight sandwich structures. Therefore, the concept of combining the auxetic honeycomb core with folded corrugations is proposed to construct a new type of corrugation star-shaped honeycomb (SSH) hybrid core for studying the dynamic behavior of sandwich panels subjected to low-velocity impact. Integrate Hertz elasticity theory and first-order shear deformation theory (FSDT) to develop an equivalent analytical model, and derive the equations of motion through Hamilton principle. To model contact force interactions during dynamic processes, a spring-mass model is utilized. Analytical solutions are derived for predicting transverse displacement with Duhamel's principle and Navier's method. Numerical simulations are conducted using the Abaqus commercial software, and the validity of the results is confirmed by comparing them with findings in the existing literature. Based on this, effective strategies for enhancing the sandwich panel's resistance to low-velocity impacts are proposed by examining the influence of different side length ratios, thickness ratios, and cell concave angles. In comparison to the corrugation re-entrant hexagonal honeycomb hybrid core sandwich panel structure, the corrugation SSH hybrid core sandwich panel structure reduces transverse displacement by 33.6 % at the same impact velocity.

与传统的轻质波纹芯材和蜂窝芯材相比，表现出负泊松比的新型蜂窝结构具有独特的机械变形特征，使其适用于轻质夹层结构建模。因此，我们提出了将辅助蜂窝芯与折叠波纹相结合的概念，以构建一种新型波纹星形蜂窝（SSH）混合芯材，用于研究夹芯板在受到低速冲击时的动态行为。综合赫兹弹性理论和一阶剪切变形理论（FSDT）建立等效分析模型，并通过汉密尔顿原理推导运动方程。利用弹簧-质量模型来模拟动态过程中的接触力相互作用。利用杜哈梅尔原理和纳维叶方法推导出预测横向位移的解析解。使用 Abaqus 商业软件进行了数值模拟，并通过与现有文献中的结果进行比较，确认了结果的有效性。在此基础上，通过研究不同边长比、厚度比和单元凹角的影响，提出了增强夹芯板抗低速冲击能力的有效策略。与波纹重入角六边形蜂窝混合芯材夹芯板结构相比，波纹 SSH 混合芯材夹芯板结构在相同冲击速度下可减少 33.6% 的横向位移。

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引用次数: 0

Application of J-integral to adhesive contact under general plane loading for rolling resistance 将 J 积分应用于一般平面载荷下的粘合接触，以获得滚动阻力

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2024-09-21 DOI: 10.1016/j.apm.2024.115700

In the present work, a mechanical model for two-dimensional non-slipping adhesive contact between dissimilar elastic solids under general loading, namely, normal forces, tangential forces and moments is proposed. The general solutions are obtained analytically with the stresses at the contact edges exhibiting oscillatory singularity, similar to those at a bimaterial interface crack. The well-known J-integral under the current context is analyzed. Its application under the selected integration contour readily gives the relationship between the stress intensity factors and energy release rates at the contact edges. With the results rolling adhesion between two solids with parabolic profiles is considered further. The applied moment can be directly determined by the difference in energy release rates at the trailing and leading edges and hence the rolling resistance even for adhesive contact with cohesive zones. These results provide the foundation for understanding some tribological phenomena associated with adhesion.

本研究提出了不同弹性固体在一般载荷（即法向力、切向力和力矩）作用下的二维非滑动粘合接触力学模型。一般解是通过分析得到的，接触边缘的应力表现出振荡奇异性，类似于双材料界面裂缝处的应力。分析了当前背景下著名的 J 积分。在选定的积分等值线下应用该积分，很容易得出接触边缘的应力强度因子和能量释放率之间的关系。根据分析结果，进一步考虑了两个具有抛物线轮廓的固体之间的滚动粘附。通过后缘和前缘能量释放率的差异，可以直接确定外加力矩，因此即使在粘附接触有内聚区的情况下，也能确定滚动阻力。这些结果为理解与粘附相关的一些摩擦学现象奠定了基础。

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引用次数: 0

Simulation of gas mixture dynamics in a pipeline network using explicit staggered-grid discretization 使用显式交错网格离散法模拟管网中的气体混合物动力学

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2024-09-20 DOI: 10.1016/j.apm.2024.115717

We develop an explicit staggered finite difference discretization scheme for simulating the transport of highly heterogeneous gas mixtures through pipeline networks. This study is motivated by the proposed blending of hydrogen into natural gas pipelines to reduce end use carbon emissions while using existing pipeline systems throughout their planned lifetimes. Our computational method accommodates an arbitrary number of constituent gases with very different physical properties that may be injected into a network with significant spatiotemporal variation. In this setting, the gas flow physics are highly location- and time- dependent, so that local composition and nodal mixing must be accounted for. The resulting conservation laws are formulated in terms of pressure, partial densities and flows, and volumetric and mass fractions of the constituents. We include non-ideal equations of state that employ linear approximations of gas compressibility factors, so that the pressure dynamics propagate locally according to a variable wave speed that depends on mixture composition and density. We derive compatibility relationships for network edge boundary values that are more complex than for a homogeneous gas. The simulation method is evaluated on initial boundary value problems for a single pipe and a small network, is cross-validated with a lumped element simulation, and used to demonstrate a local monitoring and control policy for maintaining allowable concentration levels.

我们开发了一种显式交错有限差分离散方案，用于模拟高度异质混合气体在管道网络中的传输。这项研究的动机是在天然气管道中掺入氢气，以减少最终使用过程中的碳排放，同时利用现有的管道系统在其规划的寿命期内。我们的计算方法适用于任意数量的物理性质迥异的组成气体，这些气体可能会注入具有显著时空变化的管网。在这种情况下，气体流动的物理特性高度依赖于位置和时间，因此必须考虑局部成分和节点混合。由此产生的守恒定律是根据压力、部分密度和流量以及成分的体积分数和质量分数制定的。我们采用了非理想状态方程，对气体压缩系数进行了线性近似，从而使压力动态根据取决于混合物成分和密度的可变波速进行局部传播。我们推导出了网络边缘边界值的相容性关系，这种关系比均质气体更为复杂。该模拟方法对单管和小型网络的初始边界值问题进行了评估，并与集合元素模拟进行了交叉验证，还用于演示维持允许浓度水平的局部监测和控制策略。

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引用次数: 0

A novel method for concurrent dynamic topology optimization of hierarchical hybrid structures 分层混合结构并发动态拓扑优化新方法

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2024-09-20 DOI: 10.1016/j.apm.2024.115710

This paper proposes a feature-decoupled method for concurrent dynamic topology optimization of the Hierarchical Hybrid Structure (HHS) to minimize the steady-state dynamic response. First, a novel single-variable uniform multiphase material interpolation model is established based on the Gaussian function and normalization method, which achieves the decoupled description of the macroscopic topology, substructure topology, and the spatial distribution of the substructures for HHS. Second, by combining the extended multiscale finite element method (EMsFEM), which overcomes the limitations of the scale separation assumption and periodic boundary conditions in HHS response analysis, a concurrent dynamic topology optimization mathematical formulation for HHS is constructed. Finally, the sensitivity scheme is established based on the adjoint method, and the MMA algorithm was employed to update the model. Numerical examples verify the correctness and feasibility of the proposed method, demonstrate its advantages in solving HHS concurrent topology optimization problem compared to traditional methods, and explore the impact of the number of substructure types on the optimization results of HHS.

本文提出了一种用于分层混合结构（HHS）并发动态拓扑优化的特征解耦方法，以最小化稳态动态响应。首先，建立了基于高斯函数和归一化方法的新型单变量均匀多相材料插值模型，实现了对 HHS 的宏观拓扑、子结构拓扑和子结构空间分布的解耦描述。其次，结合扩展多尺度有限元法（EMsFEM），克服了 HHS 响应分析中尺度分离假设和周期边界条件的限制，构建了 HHS 的并行动态拓扑优化数学模型。最后，基于邻接法建立了灵敏度方案，并采用 MMA 算法更新模型。数值实例验证了所提方法的正确性和可行性，展示了其在解决 HHS 并发拓扑优化问题上与传统方法相比的优势，并探讨了子结构类型数量对 HHS 优化结果的影响。

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引用次数: 0

Recovery control of autonomous underwater vehicles based on modified delay-product-type functional 基于修正的延迟积型函数的自主潜水器恢复控制

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2024-09-20 DOI: 10.1016/j.apm.2024.115713

This paper focuses on the recovery process of autonomous underwater vehicles, emphasizing a hierarchical framework in which autonomous underwater vehicles are categorized into a mothership and sub-vessels. In the recovery phase, following the completion of an underwater mission, sub-vessels navigate towards a location designated by the mothership. The crux of the recovery hinges on the design of the controller for adapting communication delays induced by environmental in underwater communication transmissions. The mothership and sub-vessels constitute a collaborative multi-autonomous underwater vehicles network equipped with these controllers, making them operate through the synchronized adjustment of their states represented in error terms. A delay-dependent controller condition criterion is proposed based on the modified delay-product-type Lyapunov-Krasovskii functional. The controller with the gain obtained from the criterion manages the system effectively and ensures successful recovery. The effectiveness of the proposed approach is demonstrated through a case study involving a network comprising one leading and four following autonomous underwater vehicles.

本文侧重于自主水下航行器的回收过程，强调自主水下航行器分为母船和子船的分层框架。在回收阶段，完成水下任务后，子船向母船指定的位置航行。回收的关键在于控制器的设计，以适应水下通信传输环境引起的通信延迟。母船和子船构成了一个多自主水下航行器协作网络，配备了这些控制器，通过同步调整误差项所代表的状态使其运行。基于修正的延迟积型 Lyapunov-Krasovskii 函数，提出了延迟相关控制器条件准则。根据该准则获得增益的控制器能有效地管理系统，并确保成功恢复。通过一个案例研究证明了所提方法的有效性，该案例研究涉及一个由 1 艘领航水下航行器和 4 艘跟航水下航行器组成的网络。

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引用次数: 0

Theoretical investigation on vibration reduction characteristics of a novel foundation metaconcrete beam 新型基础混凝土梁减振特性的理论研究

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2024-09-20 DOI: 10.1016/j.apm.2024.115679

The issue of low-frequency vibration problems in foundation beams is becoming increasingly serious. Therefore, it is imperative to find new methods for effectively reducing and controlling these low-frequency vibrations. This study proposes a novel foundation metaconcrete beam to address the challenge of low-frequency vibrations based on locally resonance theory. Additionally, an improved transfer matrix method (ITMM) is proposed to quickly and effectively calculate the bandgap of foundation metaconcrete beam. The validity of the ITMM is verified through the plane wave expansion method (PWEM), and transmission characteristics are fully analyzed using the spectral element method (SEM). Furthermore, the influences of geometric and material parameters of the foundation metaconcrete beam on band structures and transmission functions are investigated in detail. The results show that the proposed foundation metaconcrete beam exhibits multiple bandgaps, and can effectively attenuate low-frequency vibrations. These bandgaps can be tailored by appropriately adjusting relevant parameters. The foundation properties determine the formation of the first bandgap, the damping ratio of the resonator has double effects on band structures, the mass ratio of the resonator is crucial in adjusting these bandgaps, and the axial force can adjust the attenuation capability of the first bandgap.

地基梁的低频振动问题日益严重。因此，寻找有效减少和控制这些低频振动的新方法势在必行。本研究以局部共振理论为基础，提出了一种新型地基元混凝土梁来应对低频振动的挑战。此外，还提出了一种改进的传递矩阵法 (ITMM)，用于快速有效地计算地基元混凝土梁的带隙。通过平面波展开法（PWEM）验证了 ITMM 的有效性，并使用谱元法（SEM）全面分析了传输特性。此外，还详细研究了地基元混凝土梁的几何参数和材料参数对带状结构和传输函数的影响。结果表明，所提出的地基元混凝土梁具有多个带隙，能有效衰减低频振动。这些带隙可通过适当调整相关参数来定制。地基特性决定了第一个带隙的形成，谐振器的阻尼比对带隙结构有双重影响，谐振器的质量比对调整这些带隙至关重要，而轴向力可以调整第一个带隙的衰减能力。

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引用次数: 0

Decentralized learning control for high-speed trains with unknown time-varying speed delays 具有未知时变速度延迟的高速列车的分散学习控制

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2024-09-19 DOI: 10.1016/j.apm.2024.115711

Treating the multi-point-mass dynamic model of high-speed trains as an interconnected system, this study proposes a decentralized iterative learning control scheme for high-speed trains to achieve the trajectory tracking goal. By making reasonable estimates of the interaction term and compensating for it, the proposed control scheme utilizes only local information from each carriage and does not need any inter-carriage information exchange. The zero-error tracking of the desired trajectory is guaranteed even in a restricted communication environment. Considering unknown time-varying speed delays in the actual high-speed train operations, a modified decentralized iterative learning control scheme is also provided to address the negative impact of speed delays. The convergence of tracking errors is strictly proven by constructing appropriate composite energy functions. Numerical simulations further verify the theoretical results.

本研究将高速列车的多点-质量动态模型视为一个互联系统，提出了一种用于高速列车的分散迭代学习控制方案，以实现轨迹跟踪目标。通过对交互项进行合理估计和补偿，所提出的控制方案只利用每节车厢的本地信息，而不需要任何车厢间的信息交换。即使在通信受限的环境下，也能保证对所需轨迹的零误差跟踪。考虑到实际高速列车运行中未知的时变速度延迟，还提供了一种改进的分散迭代学习控制方案，以解决速度延迟的负面影响。通过构建适当的复合能量函数，严格证明了跟踪误差的收敛性。数值模拟进一步验证了理论结果。

引用次数: 0

Accelerated distributed expectation-maximization algorithms for the parameter estimation in multivariate Gaussian mixture models 多变量高斯混合模型参数估计的加速分布式期望最大化算法

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2024-09-19 DOI: 10.1016/j.apm.2024.115709

Rapid development for modeling big data requires effective and efficient methods for estimating the parameters involved. Although several accelerated Expectation-Maximization algorithms have been developed, there still exist two major concerns: reducing computational cost and improving model estimation accuracy. We propose three distributed-like algorithms for multivariate Gaussian mixture models, which can accelerate speed and improve estimation accuracy. The first algorithm is distributed algorithm, which is used to speed up the calculation of classic algorithms and improve its estimation accuracy by averaging the one-step estimators obtained from distributed operators. The second algorithm is distributed online algorithm, which is a distributed stochastic approximation procedure that performs online updates when reading online data. The final algorithm is called distributed monotonically over-relaxed algorithm, which uses an over-relaxation factor and a distributing strategy to improve the estimation accuracy of multivariate Gaussian mixture models. We investigate the stability, sensitivity, convergence, and robustness of these algorithms in a numerical study. We also apply these algorithms to three real data sets for validation.

大数据建模的快速发展需要有效和高效的方法来估算相关参数。虽然已经开发出几种加速期望最大化算法，但仍存在两大问题：降低计算成本和提高模型估计精度。我们针对多变量高斯混合模型提出了三种类似分布式的算法，既能加快速度，又能提高估计精度。第一种算法是分布式算法，用于加快经典算法的计算速度，并通过对分布式算子得到的一步估计子进行平均来提高其估计精度。第二种算法是分布式在线算法，它是一种分布式随机近似程序，在读取在线数据时执行在线更新。最后一种算法称为分布式单调过度松弛算法，它使用过度松弛因子和分布式策略来提高多元高斯混合模型的估计精度。我们通过数值研究探讨了这些算法的稳定性、敏感性、收敛性和鲁棒性。我们还将这些算法应用于三个真实数据集进行验证。

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引用次数: 0