Applied Mathematical Modelling最新文献_第4页

Synchronization analysis of a four-motor excitation with torsion spring coupling vibrating system 带扭簧耦合的四电机激振振动系统的同步分析

IF 4.4 2区工程技术

Applied Mathematical Modelling Pub Date : 2024-10-19 DOI: 10.1016/j.apm.2024.115766

Weitang Kang , Yongjun Hou , Xiaofeng Xu , Duyu Hou , Pan Fang , Wei Song , Xiangyin Li , Weibo Chen , Chuan Lu

{"title":"Synchronization analysis of a four-motor excitation with torsion spring coupling vibrating system","authors":"Weitang Kang , Yongjun Hou , Xiaofeng Xu , Duyu Hou , Pan Fang , Wei Song , Xiangyin Li , Weibo Chen , Chuan Lu","doi":"10.1016/j.apm.2024.115766","DOIUrl":"10.1016/j.apm.2024.115766","url":null,"abstract":"<div><div>In oil drilling processes, vibrating screen is a crucial solid control equipment for separating harmful solid-phase particles. However, the conventional utilization of either dual-motor or triple-motor is inadequate demanding the excitation force of large vibrating equipment. Moreover, self-synchronization in zero phase is difficult to achieve in multiple motors system. To avoid cancellation of the excitation force caused by the phase inconsistency of multiple motors, the adoption of a four-motor excitation with torsion spring coupling system is proposed this work. Initially, the mathematical model of the vibrating system is formulated through the Lagrange's equation. Subsequently, the steady-state solution is determined using Laplace transform. Then the conditions and characteristics in stable equilibrium state are elucidated employing the small parameter averaging method. Ultimately, the reliability and applicability of the theoretical results are substantiated through numerical simulations. The findings reveal that with the increase of the torsion spring stiffness, the phase difference between the motors connected by torsion springs (MCTSs) is exponentially decreased, and desired zero-phase synchronization in engineering is eventually achieved. Furthermore, the present study uncovers two distinct synchronization mechanisms in the torsion spring coupling system: mechanical controlled synchronization between MCTSs is inevitably achieved, while the self-synchronization between motors unconnected by torsion springs (MUTSs) is limited by the synchronization conditions. The study provides valuable insights for designing mechanical controlled synchronization and self-synchronization vibrating machines.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"138 ","pages":"Article 115766"},"PeriodicalIF":4.4,"publicationDate":"2024-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A heterogeneous continuum traffic flow model considering mixed connected and autonomous vehicles 考虑到混合互联和自动驾驶车辆的异构连续交通流模型

IF 4.4 2区工程技术

Applied Mathematical Modelling Pub Date : 2024-10-18 DOI: 10.1016/j.apm.2024.115765

Hanyi Li , Jianghui Wen , Min Dai

{"title":"A heterogeneous continuum traffic flow model considering mixed connected and autonomous vehicles","authors":"Hanyi Li , Jianghui Wen , Min Dai","doi":"10.1016/j.apm.2024.115765","DOIUrl":"10.1016/j.apm.2024.115765","url":null,"abstract":"<div><div>Under the background of mixed scenarios of Connected and Autonomous Vehicles and Connected and Autonomous Electric Vehicles, a novel mixed car-following model considering the information of multiple vehicles and the difference of safety spacing in different driving scenarios is proposed. Then, the corresponding heterogeneous continuum traffic flow model is derived. Secondly, through the linear and nonlinear analysis approaches, the linear stability condition and the KdV-Burgers equation are yielded to describe the characteristics of traffic flow evolution. Finally, numerical simulations are performed to explore the density evolution of traffic flow under different initial density and permeability conditions. The conclusions can be summarized as follows: (1) The derived model can well simulate spatiotemporal phase changes and traffic flow phenomena such as stop-and-go waves and local cluster effects. (2) With the increase of the permeability of electric vehicles and speed difference sensitivity coefficient, the road density decreases from 0.15veh/m to 0.06veh/m, the traffic congestion area decreases, and the traffic congestion is effectively suppressed, which also verifies the rationality of the above theory.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"138 ","pages":"Article 115765"},"PeriodicalIF":4.4,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Harmonic and superharmonic wave propagation in 2D mechanical metamaterials with inertia amplification 带惯性放大的二维机械超材料中的谐波和超谐波传播

IF 4.4 2区工程技术

Applied Mathematical Modelling Pub Date : 2024-10-18 DOI: 10.1016/j.apm.2024.115770

Marco Lepidi , Valeria Settimi

{"title":"Harmonic and superharmonic wave propagation in 2D mechanical metamaterials with inertia amplification","authors":"Marco Lepidi , Valeria Settimi","doi":"10.1016/j.apm.2024.115770","DOIUrl":"10.1016/j.apm.2024.115770","url":null,"abstract":"<div><div>An original parametric lattice model is proposed to investigate harmonic and superharmonic planar waves propagating in a two-dimensional mechanical metamaterial, whose periodic microstructure is characterized by local linkage mechanisms for pantographic inertia amplification. The free undamped dynamics in the metamaterial plane is governed by differential difference equations of motion, featuring geometric nonlinearities of both elastic and inertial nature. Within the weakly nonlinear oscillation regime, multi-harmonic wave solutions are achieved analytically, although asymptotically, by means of a suited perturbation method. At the lowest perturbation order, the linear dispersion properties (wavefrequencies and waveforms) of freely propagating monoharmonic waves are determined analytically as functions of the mechanical parameters. At higher perturbation orders, the amplitudes of the superharmonic wave components generated by quadratic and cubic nonlinearities are determined analytically, in the absence of internal resonances. Furthermore, the nonlinear corrections of the linear wavefrequencies are obtained. Smooth transitions from hardening to softening behaviors (or viceversa) are found to occur along particular propagation directions, depending on the wavelength. Physically, a pair of unexplored and interesting dynamic phenomena are disclosed. First, the free propagation of transversal waves along particular directions is characterized – independently of the wavenumber – by essentially nonlinear waveforms (<em>floppy modes</em>), featuring evanescent amplitude-dependent wavefrequency. Second, the generation of superharmonic components oscillating with double and triple frequency multiples – caused by quadratic and cubic nonlinearities – can determine a loss of polarization (<em>superharmonic depolarization</em>) in waves propagating with perfectly polarized waveforms in the linear field.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"138 ","pages":"Article 115770"},"PeriodicalIF":4.4,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Longitudinal wave propagation in FG rods under impact force 冲击力作用下 FG 棒中的纵波传播

IF 4.4 2区工程技术

Applied Mathematical Modelling Pub Date : 2024-10-18 DOI: 10.1016/j.apm.2024.115769

Xiao-Ye Dong , Xu-Hao Huang , Hai-Ting Shen

{"title":"Longitudinal wave propagation in FG rods under impact force","authors":"Xiao-Ye Dong , Xu-Hao Huang , Hai-Ting Shen","doi":"10.1016/j.apm.2024.115769","DOIUrl":"10.1016/j.apm.2024.115769","url":null,"abstract":"<div><div>A well-known fact is that one-dimensional wave analysis is the theoretical basis of the famous Hopkinson bar dynamic testing technique. The current one-dimensional wave theory is mostly confined to the slender rods of isotropic materials. It is not easy to obtain an analytical solution to the wave equation of an anisotropic rod. In this work, rods with both elastic modulus and density graded in the length direction are presented and analyzed. The one-dimensional variable coefficient wave equation corresponding to the functionally graded rod is constructed and converted into a second-order variable coefficient partial differential equation using the Laplace approach. Then, the details of solving the partial differential equation of the second-order variable coefficients are given. It is worth noting that here we construct a variable coefficient equation that satisfies the form of Euler's equation. It is still difficult to obtain analytical solutions for other equations that do not satisfy this form. Subsequently, studies of the wave propagation characteristics of rods with different graded configurations are carried out. The theoretical results show that the wave propagation behavior and post-impact vibration of the rod are significantly influenced by the graded configuration. It is possible to adjust not only the impact response at the end but also the impact response in the middle of the rod by optimizing the design of the rod's graded configuration.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"138 ","pages":"Article 115769"},"PeriodicalIF":4.4,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142654134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Strategy for obtaining robust solutions in multi-objective design with uncertainties 在具有不确定性的多目标设计中获取稳健解决方案的策略

IF 4.4 2区工程技术

Applied Mathematical Modelling Pub Date : 2024-10-18 DOI: 10.1016/j.apm.2024.115767

U. Veyna, X. Blasco, J.M. Herrero, A. Pajares

{"title":"Strategy for obtaining robust solutions in multi-objective design with uncertainties","authors":"U. Veyna, X. Blasco, J.M. Herrero, A. Pajares","doi":"10.1016/j.apm.2024.115767","DOIUrl":"10.1016/j.apm.2024.115767","url":null,"abstract":"<div><div>This paper proposes a novel definition of robustness for multi-objective optimization problems. This definition underpins an innovative strategy for obtaining robust solutions in the presence of uncertainty; it involves formulating the cost function under uncertainties as conflicting objectives during optimization. This approach aims to define the decision vectors that are not dominated in all scenarios simultaneously by any other. These solutions exhibit both optimality and robustness properties, aligning with conventional and unconventional multi-objective methods. This approach enables the implicit definition of the Pareto-optimal solutions for each scenario and robust solutions that optimize performance in worst-case scenarios. Additionally, the set of robust solutions that optimize the global performance concerning the utopian points of all uncertainty scenarios is also defined.</div><div>To demonstrate the effectiveness of this method, this paper addresses two control design problems. The first example, a first-order process, illustrates the advantages and aspects of the optimization strategy. The second problem, multi-loop temperature control design of a proton exchange membrane fuel cell stack, is a more complex engineering problem involving results from previous research.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"138 ","pages":"Article 115767"},"PeriodicalIF":4.4,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Layout optimization of pore microstructure in fluid-saturated porous media using Galerkin decoupling technology and independent continuous mapping method (GDT-ICM) 利用伽勒金解耦技术和独立连续映射法（GDT-ICM）优化流体饱和多孔介质中的孔隙微结构布局

IF 4.4 2区工程技术

Applied Mathematical Modelling Pub Date : 2024-10-16 DOI: 10.1016/j.apm.2024.115753

Hongling Ye , Sujun Wang , Jicheng Li , Yongjia Dong , Jihong Zhu

{"title":"Layout optimization of pore microstructure in fluid-saturated porous media using Galerkin decoupling technology and independent continuous mapping method (GDT-ICM)","authors":"Hongling Ye , Sujun Wang , Jicheng Li , Yongjia Dong , Jihong Zhu","doi":"10.1016/j.apm.2024.115753","DOIUrl":"10.1016/j.apm.2024.115753","url":null,"abstract":"<div><div>A layout optimal design method combining Galerkin decoupling technology and an independent continuous mapping method (GDT-ICM) is proposed to rearrange the layout of pore microstructure. Firstly, the Galerkin decoupling technology (GDT) is employed to solve the Brinkman equation for fluid flow in fluid-saturated porous media, which integrates the Stokes equation and Darcy's law. Within this framework a self-programmable element balance equation is developed. Secondly, a permeability interpolation function is defined for each element, incorporating the permeability of the fluid and pore microstructure. This function distinguishes strictly between the fluid domain and the pore domain. Pore microstructures with arbitrary shape including permeability information are established in an Euler mesh by introducing the Carman-Kozeny equation, shape functions, the Joukowski mapping and filter functions (a modified arctan mapping function and the MATLAB inpolygon function) based on the ICM method. Thirdly, a layout optimization model aiming at minimizing energy dissipation is established to accomplish the optimal distribution of pore microstructures. A sensitivity analysis is performed with respect to design variables and the optimal model is solved by a genetic algorithm. Numerical results demonstrate that the proposed method is effective and feasible in 2D-space. The maximum velocity within the fluid field is reduced by 45 %, and the issue of localized high pressure occurring around the pore is resolved. This paper provides guidance for solving the Brinkman coupled equation and the layout optimization of the microstructure in porous media.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"138 ","pages":"Article 115753"},"PeriodicalIF":4.4,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A thermal flexible rotor dynamic modelling for rapid prediction of thermo-elastic coupling vibration characteristics in non-uniform temperature fields 用于快速预测非均匀温度场中热弹性耦合振动特性的热弹性转子动态模型

IF 4.4 2区工程技术

Applied Mathematical Modelling Pub Date : 2024-10-16 DOI: 10.1016/j.apm.2024.115751

Yazheng Zhao, Jin Zhou, Mingjie Guo, Yuanping Xu

{"title":"A thermal flexible rotor dynamic modelling for rapid prediction of thermo-elastic coupling vibration characteristics in non-uniform temperature fields","authors":"Yazheng Zhao, Jin Zhou, Mingjie Guo, Yuanping Xu","doi":"10.1016/j.apm.2024.115751","DOIUrl":"10.1016/j.apm.2024.115751","url":null,"abstract":"<div><div>The flexible rotors within aero-engines operate in complex thermal environments, where temperature influences both the vibration frequency and amplitude. This study establishes a simple thermal flexible rotor dynamics model to rapidly and precisely predict thermo-elastic coupling vibration characteristics within a non-uniform temperature field. The thermal potential energy of the thermal rotor element is derived for any temperature field, and the motion equation is obtained using the Euler-Lagrange equation. Specifically, the generalized vector of an arbitrary point and cross-sectional non-uniform thermal stress of the thermal rotor element are considered in the thermal potential energy. The model's frequency error is <1 % under identical boundary conditions. Numerical findings indicate that thermal stress, temperature-dependent material properties, and the coupling effect collectively reduce the natural frequency (NF), with thermal stress having a more pronounced impact under axial constraint. Additionally, thermal stress and material decrease the amplitude across a broad range of rotation speeds, contrasting with thermal bending. This model will play a key role in the iterative calculation of thermo-elastic coupling vibration control due to its accuracy and simplicity.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"138 ","pages":"Article 115751"},"PeriodicalIF":4.4,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fault diagnosis based on incomplete sensor variables with a hierarchical semi-supervised Gaussian mixture classifier 利用分层半监督高斯混合分类器，基于不完整传感器变量进行故障诊断

IF 4.4 2区工程技术

Applied Mathematical Modelling Pub Date : 2024-10-15 DOI: 10.1016/j.apm.2024.115764

Xingchen Liu , Carman K.M. Lee , Hanxiao Zhang , Piao Chen , Jingyuan Huang , Chak Nam Wong

{"title":"Fault diagnosis based on incomplete sensor variables with a hierarchical semi-supervised Gaussian mixture classifier","authors":"Xingchen Liu , Carman K.M. Lee , Hanxiao Zhang , Piao Chen , Jingyuan Huang , Chak Nam Wong","doi":"10.1016/j.apm.2024.115764","DOIUrl":"10.1016/j.apm.2024.115764","url":null,"abstract":"<div><div>We propose a hierarchical semi-supervised variational semi-Bayesian Gaussian mixture classifier based on the partially incomplete and unlabeled samples for the fault diagnosis of mechanical and electrical systems. These systems are typically complex in structure and are monitored by multiple sensors simultaneously. Some sensor variables in the collected data may be incomplete due to sensor malfunctions or transmission errors. Additionally, labeling the data can be a time-consuming and labor-intensive task, resulting in many unlabeled samples. To address these challenges, the missing sensor variables and the unavailable labels are treated as hidden values and handled within the framework of the Expectation Maximization algorithm. We employ a semi-Bayesian technique with variational inference to estimate the model parameters. Specifically, we introduce prior distribution to the mean and covariance matrix to address the possible singularity of the empirical covariance matrix. The weighting coefficients are left without putting prior distribution so that their values can decay to zero, effectively removing redundant components of the mixture model. The factorized distribution is utilized to approximate the posterior distribution of the model parameters, as well as the missing labels and other latent variables. Numerical and real case studies are carried out to verify the effectiveness of the proposed technique.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"138 ","pages":"Article 115764"},"PeriodicalIF":4.4,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Flexural edge waves and customizable local modes of circular plates with metasurface 带元表面的圆板的挠性边缘波和可定制的局部模式

IF 4.4 2区工程技术

Applied Mathematical Modelling Pub Date : 2024-10-12 DOI: 10.1016/j.apm.2024.115749

Yizhou Shen , Pengfei Jiang , Feng Liu , Yanlong Xu , Zhichun Yang

{"title":"Flexural edge waves and customizable local modes of circular plates with metasurface","authors":"Yizhou Shen , Pengfei Jiang , Feng Liu , Yanlong Xu , Zhichun Yang","doi":"10.1016/j.apm.2024.115749","DOIUrl":"10.1016/j.apm.2024.115749","url":null,"abstract":"<div><div>In this research, we study the propagation of flexural edge waves of circular plates (also known as circular-edge waves), present design strategies of metasurfaces for manipulating these waves, and realize customizable edge modes on the basis of edge wave manipulations. Theoretical frameworks are presented to solve the dispersion relationship of circular-edge waves propagating along different boundaries, including a free edge, a strip with a weakness stiffness, and a metasurface with a slot array. On the basis of these frameworks, the propagation characteristics of circular-edge waves are revealed, and the rainbow reflection and topological interface state are realized by constructing metasurfaces. Furthermore, the modal frequency prediction, the robustness to structural parameters, and the effective excitation position for circular-edge modes are explored. Finally, based on the above analysis, the customizable local modes are presented, which means that the position of high energy regions in mode shapes can be designed without changing the corresponding modal frequency. Our work provides a new idea for the manipulation of flexural waves in circular plates and find a potential correlation between flexural waves and vibrations, which may exhibit wide applications in vibration control and acoustic device development.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"138 ","pages":"Article 115749"},"PeriodicalIF":4.4,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An adaptive time-step energy-preserving variational integrator for flexible multibody system dynamics 用于柔性多体系统动力学的自适应时间步长能量保护变分积分器

IF 4.4 2区工程技术

Applied Mathematical Modelling Pub Date : 2024-10-12 DOI: 10.1016/j.apm.2024.115759

Shuaizhen Gu, Ju Chen, Qiang Tian

{"title":"An adaptive time-step energy-preserving variational integrator for flexible multibody system dynamics","authors":"Shuaizhen Gu, Ju Chen, Qiang Tian","doi":"10.1016/j.apm.2024.115759","DOIUrl":"10.1016/j.apm.2024.115759","url":null,"abstract":"<div><div>An adaptive time-step variational integrator for simulating flexible multibody system dynamics is proposed. The integrator can adapt the time-step based on the variation of the system's energy. The flexible components in the system can undergo large overall motions and large deformations and are modelled by elements of absolute nodal coordinate formulations. In addition, a three-stage Newton-Raphson iteration method is developed to accurately solve the nonlinear discrete Euler-Lagrange equations in each time-step. Finally, three dynamic examples are presented to validate performance of the proposed integrator. Numerical results indicate that the proposed three-stage method has fast convergence rate. For the nonlinear flexible double pendulum system and the slider-crank mechanism, compared with constant time-step integrators, the proposed integrator can preserve the system's total energy more accurately and lead to more accurate dynamic responses. For the contact problem, the proposed integrator can quickly change the time-step size based on the sudden changes of energy to precisely compute the contact force and dynamic responses. Moreover, the proposed integrator can exactly preserve the displacement constraints and the velocity constraints simultaneously. In addition, it is noted that the computation efficiency of the proposed integrator needs to be further improved.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"138 ","pages":"Article 115759"},"PeriodicalIF":4.4,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0