Dynamic Effective Properties of Lead-Reinforced Epoxy Resin Composites with Differential Method by Haitao Zhu, Yongping Wan

“…The corresponding differential equations are numerically solved by the fourth-order Runge–Kutta method, and the dynamic effective modulus and density are obtained. …”
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BIFURCATION ANALYSIS AND COEXISTENCE OF MULTIPLE ATTRACTORS OF A ROLLING BEARING-ROTOR SYSTEM by AN HuiNing, JIN Hua, Lü XiaoHong, WANG Xin

“…Taking the unbalanced rotor system supported by rolling bearings as the research object, the variable step size Runge-Kutta method is used for numerical integration to obtain the dynamic response of the rotor system. …”
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Analysis of Vibration Characteristic of the ZC1 Worm Gear Reducer by Ma Yujuan, Ji Weixi, Song Lijuan, Jin Xiaoma

“…Based on the theory of the lumped mass method,the dynamical analysis model of the ZC1 worm gear reducer transmission system is established. The Runge-Kutta method is used to solve the normalized equations in MATLAB,and the dynamic response curve of the system is obtained. …”
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Dynamics Analysis and Chaos Control of Multi-nonlinear Coupling System for PMSM-2R Mechanism by Cao Shulei Xie Jin Ding Weigao

“…Based on bond graph, a modern modeling method for multi-energy domain coupling system, a mathematical model of multi-nonlinear coupling system of PMSM-2R mechanism is established and solved by Runge-Kutta method. In the coupled system, the effects of the coupling between multi-nonlinear systems on the dynamic characteristics of the system are analyzed by the two-parameter chaotic edge method, bifurcation diagram and the maximum Lyapunov exponent. …”
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Similarity analysis for natural convection from a vertical plate with distributed wall concentration by I. Mulolani, M. Rahman

“…Numerical results, based on the fourth order Runge-Kutta method, for Schmidt number ranging from 0.0 to 100.0 and reaction order from 0.0 to 1.5 are presented. …”
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Research of the Transmission Error of Planetary Transmission System for Hub Motor by Chen Haoran, Qin Xunpeng, Zhang Jiang

“…Taking the planetary transmission system of hub motor as the research object,the kinematic differential equations of the system are established by considering the influence factors of time-varying mesh stiffness,meshing phase and equivalent mesh error,and the Runge-Kutta method is used to get the system transmission error. …”
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Recoil and Vibration in an Archery Bow Equipped with a Multi-Rod Stabilizer by Igor Zaniewski

“…The research methods are based on the Euler-Bernoulli theory of beam bending, Lagrange equations of the second kind, the Cauchy problem, and the Runge-Kutta method. A mathematical software package was used to analyze the problem. …”
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The Motion of a Rigid Body with Irrational Natural Frequency by A. I. Ismail

“…Using the digital fourth-order Runge-Kutta method, we determine the digital solutions of the obtained system. …”
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Dynamics Analysis of Helical Gear with Time-varying Stiffness and Tooth Pitch Error by Zhang Liu, Wu Xuncheng, Xu Junjian, Zhang Juecheng, Zhang Yanjie

“…Combining with the internal incentives,such as the tooth pitch error,the shaft coupling nonlinear dynamics model of helical gear pair bending and twisting is established. The Runge-kutta method is used for numerical solution,the time-domain response curves and the frequency spectrum diagrams of the vibration response of a helical gear pair are obtained. …”
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Numerical Approximation of Compressible Two-Phase Six-Equation Model Using CE/SE and RKDG Schemes by Omar Rabbani, Saqib Zia, Munshoor Ahmed, Asad Rehman, Ilyas Khan, Mulugeta Andualem

“…The results are compared with the exact solution and also with Runge-Kutta Discontinuous Galerkin (RKDG) and central (NT) schemes.…”
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Modeling and dynamic analysis of split torsion transmission system considering backlash and center distance errors by Jingwei Ding, Guanghu Jin

“…In this context, a nonlinear dynamic equation was formulated in the present study for a single-input dual-output gear split-torque transmission system, and the system’s dynamic behavior was examined under the effects of center distance error and backlash using the fourth-order Runge-Kutta method. The findings indicate that the impact of center distance error on the system’s dynamics is linear, whereas the effect of backlash is nonlinear. …”
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NONLINEAR RESPONSE ANALYSIS OF DOUBLE DISK RUBBING ROTOR-OIL FILM BEARING SYSTEM by LIU JunJie, ZHANG LingYun, YI FengWei, QIN ZeFeng

“…In order to describe rotor-bearing system more accurately and to consider the influence of nonlinear oil film force and rubbing force,this paper establishes a single disk rubbing rotor-bearing system model with nonlinear support,and deduces the dimensionless motion equation of the system.The four-order runge-kutta method was used to numerically calculate the equation.The bifurcation diagram,axis trajectory diagram,Poincare cross section diagram and maximum rubbing force diagram were comprehensively used to study the dynamic behavior of the system,and the influence of eccentricity and rotation speed on the nonlinear dynamic characteristics of the system was analyzed.The analysis results show that with the decrease of eccentricity and the increase of rotating speed ratio,the rubbing force between rotating stator will also decrease,the chaotic region of the system will also decrease,and the system is in periodic motion,thus the stability of the system can be improved.…”
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ANALYSIS OF NONLINEAR DYNAMIC CHARACTERISTICS OF AN IMPACT-UNBALANCED SUSPENDED ROTOR SYSTEM by LIU JunJie, ZHANG LingYun, MA ShaoHui, LAN HaiPeng, ZHANG YouQiang

“…Established an impact-unbalanced suspended rotor system mechanics models, and the dimensionless motion equation of system is deduced, using the fourth order Runge-Kutta method for the numerical calculation of this model, the integrated use of bifurcation diagram, orbit diagram, Poincare section diagram, the axis displacement time history diagram, maximum moment diagram and duty ratio diagram study the dynamic behavior of the system, identify the impact of the rotor, the maximum torque and impact by the proportion of time, and analyzed the speed ratio and the change of the stiffness coefficient of the influence of the nonlinear dynamic characteristics of the system.The analysis results show that the system presents chaotic motion in a certain parameter domain at the medium velocity stage, while the system tends to stable periodic motion in other parameter domains.With the increase of the stiffness coefficient, the chaotic motion region and the maximum moment of the system increase, and the stability of the system decreases.…”
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Nonlinear Parametric Vibration and Chaotic Behaviors of an Axially Accelerating Moving Membrane by Mingyue Shao, Jimei Wu, Yan Wang, Qiumin Wu

“…However, the solutions concerning to differential equations are determined through the 4th order Runge–Kutta technique. The results of mean velocity, velocity variation amplitude, and aspect ratio on nonlinear vibration of moving membranes are emphasized. …”
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A High-Precision Calculation Method for Internal Trajectory of Underwater Weapon Launch by Chun YANG, Kaifu LI, Weibin CHEN, Lutian LI, Yinlong LI

“…The method combined high-precision theoretical derivation with computational fluid mechanics slip technique and used the fourth-order Runge-Kutta method to solve the high-pressure gas domain during the launch process. …”
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Control of Limit Cycle Oscillation in a Three Degrees of Freedom Airfoil Section Using Fuzzy Takagi-Sugeno Modeling by Douglas Domingues Bueno, Luiz Carlos Sandoval Góes, Paulo José Paupitz Gonçalves

“…Time simulations with different initial conditions are performed using a modified Runge-Kutta algorithm to compare the system with and without control forces. …”
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Clinical and Laboratory Parameters of Metabolic Syndrome in Chronic Spontaneous Urticaria: A Cross-Sectional Study by M. Thanoj K. Reddy, Seetharam A. Kolalapudi, Seva Praveen, Subhashini Konala, Gunnam L. Rasajna, Saloni S. Khutate

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Analysis on the Synergy Evolutionary Development of the Collecting, Distributing, and Transporting System of Railway Heavy Haul Transportation by Fenling Feng, Dan Lan, Liuwen Yang

“…Then spline interpolation method, numerical differential five-point formula, and method of least squares are used to solve synergistic coefficient, while fourth-order Rugge-kutta method and fourth-order Adams linear implicit formula method are used to solve coevolutionary curve of the system. …”
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Structural Design and Performance Analysis of a Three-dimensional Braided Two-stage Reducer Box by Zhang Weiliang, Wang Xupeng, Ji Xiaomin, Tang Xinyao, Liu Fengfeng, Liu Mingjun

“…Under the assumption of ignoring the influence of friction, bearing and other factors on the system, the motion equations of the two-stage gear transmission system with a box body were established, and the numerical analysis of the two-stage gear transmission system was carried out by the Runge-Kutta method to study the influence of excitation on the dynamic characteristics of the assembling and weaving system.…”
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Convergent Power Series of sech⁡(x) and Solutions to Nonlinear Differential Equations by U. Al Khawaja, Qasem M. Al-Mdallal

“…A detailed comparison with the fourth-order Runge-Kutta method and extensive analysis of the behavior of the error and CPU time are performed.…”
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