ANALYSIS OF ELECTROMECHANICAL COUPLING DYNAMIC CHARACTERISTICS OF SERVO DRIVE SYSTEM by LI WenLi, LIU YongKang, GUO Dong, LU Yu, SHI XiaoHui, ZHENG WeiDong

“…In order to explore the influence of the changes of electromagnetic parameters and mechanical parameters on the dynamic characteristics of servo drive system,based on the relevant theories of mechanical dynamics and electromagnetism,builded a four-inertia electromechanical coupling model including motor electromagnetic stiffness and electromagnetic damping.Obtained the time history curve,phase plane diagram,Poincare mapping and amplitude-frequency characteristic curve of the system by using 4～5 order Runge-Kutta method with variable step size. Analyzed effects of the changes of electromagnetic stiffness,excitation frequency and transmission comprehensive error on the motion state of the electromechanical coupling system.Under different electromagnetic stiffness values,the system will change from period doubling bifurcation to period 1 motion,and then to chaotic motion,and when the electromagnetic stiffness decreases from 5 × 10~5 Nm/rad to 10~5 Nm/rad,the maximum amplitude of the system will increase by 7%. …”
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Chaotic Dynamics of a Mixed Rayleigh–Liénard Oscillator Driven by Parametric Periodic Damping and External Excitations by Yélomè Judicaël Fernando Kpomahou, Laurent Amoussou Hinvi, Joseph Adébiyi Adéchinan, Clément Hodévèwan Miwadinou

“…Bifurcation structures of our system are performed through the fourth-order Runge–Kutta ode 45 algorithm. It is found that the system displays a remarkable route to chaos. …”
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Research of Nonlinear Dynamic Characteristics of Shield Machine Multilevel Planetary Gear Train by Ren Jianqing, Yu Qinghuan, Yao Jiantao, Sun Xiaoyu

“…Then based on the dimensionless differential equations of four orders variable step Runge Kutta method. The transmission mechanism of the phase diagram,Poincare diagram are got,by changing the amplitude of excitation and the meshing stiffness,the influence of parameter variation on the nonlinear characteristics of the system is analyzed. …”
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Study on dynamics characteristic on combination misalignment and rubbing of the dual-rotor system by YAO Xia, NAN Guofang, LI Yao, QIU Xuewen

“…The misalignment of the dual-rotor system for the aero-engine will lead to abnormal increase of the vibration which results in the rotor-stator rubbing and affects the safty and stability of the rotor operation.The dual-rotor system was taken as the research object.Considering the combination misalignment-rubbing fault, the dynamic model of the rotor system is established based on the lumped mass method.The differential equation of the system motion was established according to the Lagrange equation, and the Range-Kutta method was used to solve it.The influence mechanism of the key parameters such as the speed, the misalignment angle and the coupling misalignment on the nonlinear dynamic characteristics of the system was studied.The results show that the system presents complex dynamic characteristics such as periodic, multi-periodic, quasi-periodic and chaotic motion with the increase of the rotor’s speed.When the speed is in the range of 1 500-2 200 rad/s, the system switches between periodic 2 motion and chaotic state through multiple paroxysmal bifurcations and paroxysmal inverted bifurcations.There are nonlinear phenomena such as jump in the bifurcation diagram of the vibration response with the change of the parallel misalignment of the coupling.As the misalignment angle of the bearing increases, the chaotic interval of the high speed decreases, and the stable periodic motion interval increases.…”
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A Vibration Model of Ball Bearings with a Localized Defect Based on the Hertzian Contact Stress Distribution by Fanzhao Kong, Wentao Huang, Yunchuan Jiang, Weijie Wang, Xuezeng Zhao

“…The relative motion between the inner ring, the outer ring, and the balls is considered in the proposed model, and the Runge-Kutta algorithm is used to solve the vibration equations. …”
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NONLINEAR DYNAMICS ANALYSIS OF A SINGLE-DISK FLEXIBLE RUBBING ROTOR by LIU DeQiang

“…Based on the mechanical model of a single-disk flexible Jeffcott rotor,the fourth-order Runge-Kutta method with variable step size was used for numerical simulation. …”
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ANALYSIS OF DYNAMIC CHARACTERISTICS OF FAULTY MAGNETIC BEARING-ROTOR SYSTEM by ZHANG LingYun, ZOU AiCheng

“…Consider the coupling of shaft cracks, rotor eccentricity, electromagnetic force of the electromagnetic bearing, and friction force between the rotating shaft and auxiliary bearing, the Runge-Kutta method is used to obtain the electromagnetic bearing-rotor system under different fault conditions. …”
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Influence of Stochastic Meshing Parameter on Vibration of Shearer Cutting Unit Planetary by Wu Guijun, Zhang Yu, Chen Hongyue, Mao Jun

“…In order to research the influence of stochastic meshing parameters on vibration of shearer cutting unit gear transmission system,taking the MG500/1180-WD shearer as the research object,considering about the effects of the factors such as meshing stiffness,meshing damping,combined error and gear backlash,the pure torsion nonlinear dynamics model of gear transmission system for shearer cutting unit is established,takes the meshing stiffness,meshing damping,combined error and gear backlash as the random variable,and also using the variable step size Runge-Kutta methods,the system model is solved,the statistical characteristic for the transient response of the system is obtained through statistic analysis. …”
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Study on Dynamics of Wind Turbine Gearbox with Crack Fault under Random Wind Load by Jinwen Wang, Xiayue Ma, Zihao Liu, Xiaolu Leng, Shijing Wu

“…The translation-torsional-axial coupling model of wind turbine gearbox is established by using the lumped parameter method and considering backlash，time-varying meshing stiffness，meshing error parameter. The Runge-Kutta method is adopted to get the system dynamics response，and the order analysis of the response is carried out. …”
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Advanced Method for Calculations of Core Burn-Up, Activation of Structural Materials, and Spallation Products Accumulation in Accelerator-Driven Systems by A. Stankovskiy, G. Van den Eynde

“…Secondly, it uses a state-of-the-art numerical solver for the first-order ordinary differential equations describing the isotope balances, namely, a Radau IIA implicit Runge-Kutta method. The versatility of the code allows using it for time behavior simulation of various systems ranging from single pin model to full-scale reactor model, including such specific facilities as accelerator-driven systems. …”
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Hierarchical Modeling and Dynamic Analysis of Hoist System in Electric Mining Shovel by Wei Sun, Jianan Du, Lintao Wang, Penglong Luan, Jie li

“…Under the ripple drive torque simulated by Simulink, the dynamic characteristics of the hoist system in time domain and frequency domain were obtained using numerical integration with the Runge–Kutta method in Matlab. At last, the model validity was verified by contrasting the responses under actual test and the model. …”
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Dropping Shock Characteristics of the Suspension Cushioning System with Critical Components by Hui Li, Anjun Chen, Ningning Duan

“…The numerical results of shock response were gained using Runge-Kutta method. To evaluate the dropping shock characteristics of critical components, the dropping damage boundary curve was established, where the system parameter and the dimensionless shock velocity were selected as two coordinate parameters. …”
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Development of an Impact Energy Absorption Structure by an Arc Shape Stroke Origami Type Hydraulic Damper by Jingchao Guan, Yuan Yao, Wei Zhao, Ichiro Hagiwara, Xilu Zhao

“…A nonlinear dynamics governing equation was established using the derived formula for the damping force of the origami hydraulic damper, and a numerical analysis using the Runge–Kutta method was established. An impact test device with an arc-shaped stroke was developed, and the error between the numerical analysis value of the impact displacement and the measured experimental value was confirmed to be sufficiently small. …”
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A Novel Parabolic Trough Concentrating Solar Heating for Cut Tobacco Drying System by Jiang Tao Liu, Ming Li, Qiong Fen Yu, De Li Ling

“…A cut tobacco drying mathematical model calculated by fourth-order Runge-Kutta numerical solution method was used to simulate the cut tobacco drying process. …”
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The significance of magnetized thermal radiation on the magnetohydrodynamic (MHD) behavior of Williamson hybrid ferrofluids over a stretching sheet by D. Thenmozhi, M. Eswara Rao, P.D. Selvi, RLV. Renuka Devi, S. Kiranmaiye, Ch. Nagalakshmi

“…These governing equations are transformed into ordinary differential equations (ODEs) via similarity transformations and solved numerically using the Runge-Kutta (R-K) 4th-order method coupled with the shooting technique. …”
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Numerical Simulation of Dynamic Response of Submerged Floating Tunnel under Regular Wave Conditions by Wenlong Luo, Bo Huang, Yao Tang, Hao Ding, Ke Li, Liang Cheng, Qingyang Ren

“…In this model, wave-induced hydrodynamic loads are estimated by the Morison equation for a moving object, and the simplified governing differential equation of the tunnel with mooring cables is solved using the fourth-order Runge–Kutta and Adams numerical method. The numerical results are successfully validated by direct comparison against published experimental data. …”
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Experimental validation of the analytical modelling of a digitally created duffing acoustic nonlinear oscillator at low amplitudes by Morell Maxime, Collet Manuel, Gourdon Emmanuel, Ture Savadkoohi Alireza, De Bono Emanuele

“…The experimental implementation is done using a real-time-based algorithm retrieving the measured pressure from a microphone and giving the electrical current to send to a loudspeaker as an output thanks to a Runge-Kutta-like algorithm. Despite the several assumptions of the model, the analytical modelling is validated by the experiment, showing that the model is able to predict the two-degree-of-freedom system.…”
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Nonlinear Dynamic Characteristics of Multidisk Rod Fastening Rotor with Axial Unbalance Mass Distribution by Li Zhao, Haosui Zhang, Yibing Liu, Chao Zhou

“…The fourth-order Runge-Kutta method was used to solve the model, and the spectrum and axis trajectory curves were obtained. …”
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Swarming Computational Procedures for the Coronavirus-Based Mathematical SEIR-NDC Model by Suthep Suantai, Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Watcharaporn Cholamjiak

“…The correctness of the stochastic computing scheme performances is verified by using the comparison of the obtained performances of the mathematical SEIR-NDC system and the reference Runge–Kutta scheme. Furthermore, the graphical illustrations of the performance indices, absolute error, and convergence curves are derived to validate the robustness of the proposed ANN-PSOSQP approach for the mathematical SEIR-NDC system.…”
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Modeling and Analysis of HIV and Cholera Direct Transmission with Optimal Control by Kumama Regassa Cheneke, Koya Purnachandra Rao, Geremew Kenassa Edessa

“…The optimal system is solved numerically using forward and backward sweep method of Runge Kutta’s fourth-order methods. The numerical simulations are plotted using MATLAB.…”
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