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Numerical Simulation of Nonlinear Dynamical Systems
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Numerical Simulation of Nonlinear Dynamical Systems

A special issue of Processes (ISSN 2227-9717). This special issue belongs to the section "Process Control and Monitoring".

Deadline for manuscript submissions: closed (30 August 2023) | Viewed by 29423

Special Issue Editors

Prof. Dr. Liming Dai

E-Mail Website
Guest Editor
Industrial Systems Engineering, University of Regina, Regina, SK S4S 0A2, Canada
Interests: nonlinear dynamics; numerical methods and simulations of nonlinear dynamic systems; diagnosis of nonlinear characteristics; response prediction of nonlinear systems
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Jialin Tian

E-Mail Website
Guest Editor
School of Mechanical Engineering, Southwest Petroleum University, Chengdu 610500, China
Interests: mechanical nonlinear dynamics and control; modern design theory and methods of oil and gas equipment; downhole tools and drill bit technology; downhole testing and intelligent control
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Numerical simulation is an important approach for solving nonlinear dynamic systems, and it is a unique and feasible method for solving and analyzing nonlinear systems in many cases. With the development of science and technology, conventional approaches show difficulties in understanding the world, which is complex and nonlinear in general. Moreover, more and more nonlinear and complex systems need to be solved and analyzed with high accuracy, efficiency, and reliability.

With the dramatic developments in science and technology, greater numbers of nonlinear and complex systems appear and need to be solved with sufficient accuracy and reliability. In addition, in order to analyze and evaluate the nonlinear dynamic systems, to optimize system and operation parameters, and to improve the accuracy and reliability of the numerical results of the nonlinear dynamic systems, highly efficient numerical methods and numerical simulation approaches are demanded. The dependable and scientifically sound modelling of the nonlinear dynamic systems, in reflecting physical models and implementing mathematical models, is also a serious challenge facing scientists and researchers in numerically solving and simulating nonlinear dynamic systems. Due to the approximation, accumulation of calculation errors, and other inherent difficulties embedded in numerical calculations and simulations and the software packages utilized in numerical simulations, highly effective control strategies are necessary in order to ensure the accuracy and reliability required for the numerical simulations—especially those for nonlinear multidimensional systems.

Reflecting and addressing the challenges and demands as indicated, this Special Issue on “Numerical Simulation of Nonlinear Dynamical Systems” aims to provide a platform for researchers, scientists, engineers, and others active or interested in numerical simulations for nonlinear dynamic systems to present and exchange their research progresses, new discoveries and developments, and applications in the field. The topics of the Special Issue include, but are not limited to:

  • Theoretical progress in numerical simulations for nonlinear dynamic systems;
  • Innovative numerical methods for solving and analyzing dynamic systems in nonlinear science;
  • Mathematical and numerical modelling of nonlinear dynamic systems found in the fields of science and engineering;
  • Nonlinear phenomena of dynamic systems and diagnosis of the nonlinear behavior of the systems;
  • Theoretical development and analysis of nonlinear dynamic systems;
  • Experimental observation and measurements of nonlinear dynamic systems found in science and engineering;
  • Hamiltonian systems and applications in nonlinear dynamic systems;
  • Synchronization and control strategies for nonlinear dynamic systems;
  • Analysis of nonlinear dynamic systems in biological physics;
  • Safety analysis of nonlinear dynamic systems.

Prof. Dr. Liming Dai
Prof. Dr. Jialin Tian
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Processes is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • numerical simulations
  • nonlinear dynamic systems
  • numerical methods for nonlinear systems
  • linear and nonlinear dynamics
  • nonlinear behavior characterization
  • nonlinear dynamic system diagnosis
  • modelling of nonlinear dynamic systems
  • safety and control of nonlinear dynamic systems

Published Papers (18 papers)

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Research

12 pages, 3043 KiB  
Article
Vibration Characteristics and Location of Buried Gas Pipeline under the Action of Pulse Excitation
by Baoyong Yan, Jialin Tian, Xianghui Meng and Zhe Zhang
Processes 2023, 11(10), 2849; https://doi.org/10.3390/pr11102849 - 27 Sep 2023
Cited by 1 | Viewed by 663
Abstract
In this paper, the attenuation of sound waves in underground gas pipelines and the vibration characteristics of pipelines are studied, and the feasibility and effectiveness of acoustic measurement of PE pipelines are verified. In this paper, the attenuation equation of sound waves in [...] Read more.
In this paper, the attenuation of sound waves in underground gas pipelines and the vibration characteristics of pipelines are studied, and the feasibility and effectiveness of acoustic measurement of PE pipelines are verified. In this paper, the attenuation equation of sound waves in an underground gas transmission pipeline is derived based on the propagation characteristics of gas and the vibration characteristics of the pipeline itself. In order to verify the experimental results, we conducted an experimental test on the air pipeline model and verified the feasibility and effectiveness of the acoustic measurement of the PE pipeline through the test under the action of pulse excitation. Then, we detect the background noise, design the test scheme according to the characteristics of the buried pipeline, and select the test site for field test. In the test process, we collected the test data and obtained the spectrum diagram of the test data by fast Fourier transform (FFT). By analyzing the results of the spectrogram, we find that the pulse signal can penetrate the medium composed of the pipe formation, but the amplitude of the sound will be sharply attenuated. At the same time, according to the size of the peak in the spectrum, we can determine the location of the pipe. In summary, the feasibility and effectiveness of acoustic measurement of the PE pipeline are verified through experimental tests, and attenuation equations based on acoustic wave propagation characteristics and pipeline vibration characteristics are proposed. It has important practical application value for the safety monitoring and positioning of the buried gas pipeline. Full article
(This article belongs to the Special Issue Numerical Simulation of Nonlinear Dynamical Systems)
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15 pages, 8722 KiB  
Article
Numeric Investigation on the Stability of a Preformed Roadway under Backfill Body Subjected to Blasting Load
by Hongwei Deng, Fei Wu and Renze Ou
Processes 2023, 11(9), 2548; https://doi.org/10.3390/pr11092548 - 25 Aug 2023
Viewed by 646
Abstract
Tungsten, essential in the industrial, military, and civilian domains and deemed a strategic resource by various nations, necessitates careful consideration in room and pillar mines due to the potential instability and safety hazards posed by untouched mine pillars, making tungsten recovery crucial for [...] Read more.
Tungsten, essential in the industrial, military, and civilian domains and deemed a strategic resource by various nations, necessitates careful consideration in room and pillar mines due to the potential instability and safety hazards posed by untouched mine pillars, making tungsten recovery crucial for worker safety and economic gain. This research aims to provide guidance for recovering tungsten from mine pillars and making mining operations safer for workers in the Xianglushan mine. Numerical simulations are conducted to study the mechanical response of a preformed roadway in a backfill body subjected to static and dynamic loads with various explosive distances and positions. Blasting vibration velocity and blasting-induced damage in the backfill body are extracted to evaluate the mechanical response of the backfill body. The numerical results indicate that the steel frame and preformed roadway remain stable under the influence of both gravity and the impact from blasting, using a charge of 3.00 kg per blasthole. By analyzing these indicators, potential safety hazards in the backfill body and preformed roadway are identified, and the numerical results provide guidance for mine pillar recovery practices. Full article
(This article belongs to the Special Issue Numerical Simulation of Nonlinear Dynamical Systems)
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16 pages, 3265 KiB  
Article
Extended Runge-Kutta Scheme and Neural Network Approach for SEIR Epidemic Model with Convex Incidence Rate
by Ahmed A. Al Ghafli, Yasir Nawaz, Hassan J. Al Salman and Muavia Mansoor
Processes 2023, 11(9), 2518; https://doi.org/10.3390/pr11092518 - 22 Aug 2023
Cited by 1 | Viewed by 876
Abstract
For solving first-order linear and nonlinear differential equations, a new two-stage implicit–explicit approach is given. The scheme’s first stage, or predictor stage, is implicit, while the scheme’s second stage is explicit. The first stage of the proposed scheme is an extended form of [...] Read more.
For solving first-order linear and nonlinear differential equations, a new two-stage implicit–explicit approach is given. The scheme’s first stage, or predictor stage, is implicit, while the scheme’s second stage is explicit. The first stage of the proposed scheme is an extended form of the existing Runge–Kutta scheme. The scheme’s stability and consistency are also offered. In two phases, the technique achieves third-order accuracy. The method is applied to the SEIR epidemic model with a convex incidence rate. The local stability is also examined. The technique is evaluated compared to existing Euler and nonstandard finite difference methods. In terms of accuracy, the produced plots show that the suggested scheme outperforms the existing Euler and nonstandard finite difference methods. Furthermore, a neural network technique is being considered to map the relationship between time and the amount of susceptible, exposed, and infected people. Full article
(This article belongs to the Special Issue Numerical Simulation of Nonlinear Dynamical Systems)
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17 pages, 8336 KiB  
Article
The Non-Linear Excitation Load-Sharing Method of a High-Powered Nuclear Planetary Gear Train
by Fude Wei, Qingbing Dong, Huanhuan Wang and Shuncheng Yang
Processes 2023, 11(7), 2190; https://doi.org/10.3390/pr11072190 - 21 Jul 2023
Viewed by 742
Abstract
The paper primarily employs the 3D calculation method of the helical gear-meshing line and meshing position, in addition to the traditional method of the gear-meshing stiffness calculation. This analysis and correction of load-sharing are beneficial for improving the assembly process of high-powered critical [...] Read more.
The paper primarily employs the 3D calculation method of the helical gear-meshing line and meshing position, in addition to the traditional method of the gear-meshing stiffness calculation. This analysis and correction of load-sharing are beneficial for improving the assembly process of high-powered critical equipment. The dynamic models of rigid–flexible coupling, velocity–torque, and the meshing force of planetary gear trains in nuclear power plants are established based on the principles of gear dynamic characteristics. Based on an analysis of the vibration characteristics of a planetary gear train, a load-sharing method for the planetary gear train is proposed. This uniform load-sharing method is explored under different modification values to provide a reference for load-sharing research on high-powered key equipment. In this paper, a dynamic simulation analysis of the gearbox system is conducted, using virtual prototype software to study the load-sharing performance of the planetary gear system. Furthermore, via a vibration frequency analysis of the gear mesh force, the causes of planetary gear train vibration are discussed, particularly their impact on planetary load. This provides a basis for the assembly process of a nuclear power circulation pump gearbox, ensuring that the gearbox for the circulation pump has a longer life that meets the 40-year service life requirement, and provides a foundation for the study of planetary load characteristics. Full article
(This article belongs to the Special Issue Numerical Simulation of Nonlinear Dynamical Systems)
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17 pages, 693 KiB  
Article
Finite-Difference Hermite WENO Scheme for Degasperis-Procesi Equation
by Liang Li, Yapu Feng, Yanmeng Wang, Liuyong Pang and Jun Zhu
Processes 2023, 11(5), 1536; https://doi.org/10.3390/pr11051536 - 17 May 2023
Viewed by 935
Abstract
We present a fifth-order finite-difference Hermite weighted essentially non-oscillatory (HWENO) method for solving the Degasperis–Procesi (DP) equation in this paper. First, the DP equation can be rewritten as a system of equations consisting of hyperbolic equations and elliptic equations by introducing an auxiliary [...] Read more.
We present a fifth-order finite-difference Hermite weighted essentially non-oscillatory (HWENO) method for solving the Degasperis–Procesi (DP) equation in this paper. First, the DP equation can be rewritten as a system of equations consisting of hyperbolic equations and elliptic equations by introducing an auxiliary variable, since the equations contain nonlinear higher order derivative terms. Then, the auxiliary variable equations are solved using the Hermite interpolation, while the HWENO scheme is performed for the hyperbolic equations. Compared with the popular WENO-type scheme, the most important feature of the HWENO scheme mentioned in this paper is the compactness of its spatial reconstruction stencil, which can achieve the fifth-order accuracy of the expected design with only three points, while the WENO method requires five points. Finally, we demonstrate the effectiveness of the HWENO method in various aspects by conducting some benchmark numerical tests. Full article
(This article belongs to the Special Issue Numerical Simulation of Nonlinear Dynamical Systems)
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17 pages, 4560 KiB  
Article
Prediction and Control of Input and Output for Industry–University–Research Collaboration Network in Construction Industry
by Ruiqiong Zhong, Dong Wang, Cheng Hu, Yuxin Li and Gege Feng
Processes 2022, 10(10), 2037; https://doi.org/10.3390/pr10102037 - 9 Oct 2022
Cited by 4 | Viewed by 1190
Abstract
An unreasonable allocation of resources has led to a low rate of output in the industry–university–research collaboration network. A solution to this problem is to control and predict the input and output. However, the network has the characteristics of strong nonlinearity and insufficient [...] Read more.
An unreasonable allocation of resources has led to a low rate of output in the industry–university–research collaboration network. A solution to this problem is to control and predict the input and output. However, the network has the characteristics of strong nonlinearity and insufficient samples. It is difficult for the existing control methods to migrate to collaboration networks because the traditional control methods, including Proportional–Integral–Derivative (PID) control and Model Predictive Control (MPC), are usually not applied to the system with strong nonlinearity and the controlled system needs to have specific parameters, while the modern control methods, including feedforward control and feedback control, have their limitations in both parameters and other aspects. In addition, there is a lack of research on the control and output prediction of collaboration networks, and there is no effective and applicable scheme for the control and prediction. Considering the nonlinearity and insufficient samples of the collaboration network, a Feedforward Control–Feedback Control Model based on the Multi-Layer Perceptron (FCFCM-MLP) is proposed in this paper. Adopting the controller structure of the Grid Search-Multilayer Perceptron (GS-MLP), a control block diagram, a feedforward controller, a feedback controller, and prediction methods such as Harris Hawk Optimization-Support Vector Regression (HHO-SVR) are designed for the FCFCM-MLP, which effectively realizes the feedforward control, feedback control, and prediction of inputs and outputs. In this paper, simulation tests on output-feedback tracking control are conducted with real statistics of papers jointly produced by the industry–university–research collaboration network in the construction industry. The results show that the proposed model has obvious effectiveness. Specifically, compared with the model composed of other controller structures and prediction methods, the optimal model Particle Dynamic Multiple Perturbation_Butterfly Optimization Algorithm-Support Vector Regression_Grid Search-Multi-Layer Perceptron (PDM_BOA-SVR_GS-MLP) obtained in this paper can minimize the predictive control error and effectively improve the control accuracy. Full article
(This article belongs to the Special Issue Numerical Simulation of Nonlinear Dynamical Systems)
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33 pages, 6990 KiB  
Article
New Directions in Modeling and Computational Methods for Complex Mechanical Dynamical Systems
by Firdaus E. Udwadia and Nami Mogharabin
Processes 2022, 10(8), 1560; https://doi.org/10.3390/pr10081560 - 9 Aug 2022
Cited by 1 | Viewed by 1281
Abstract
This paper presents a new conceptualization of complex nonlinear mechanical systems and develops new and novel computational methods for determining their response to given applied forces and torques. The new conceptualization uses the idea of including particles of zero mass to describe the [...] Read more.
This paper presents a new conceptualization of complex nonlinear mechanical systems and develops new and novel computational methods for determining their response to given applied forces and torques. The new conceptualization uses the idea of including particles of zero mass to describe the dynamics of such systems. This leads to simplifications in the development of their equations of motion and engenders a straightforward new computational approach to simulate their behavior. The purpose of the paper is to develop a new analytical and computational methodology to handle complex systems and to illustrate it through the study of an old unsolved problem in classical mechanics, that of a non-uniform rigid spherical shell rolling, without slipping, under gravity on an arbitrary dimpled bowl-shaped rigid surface. The new conceptualization provides the explicit equations of motion for the system, the analytical determination of the reaction forces supplied by the surface, and a straightforward computational approach to simulate the dynamics. Detailed analytical and numerical results are provided. The computations illustrate the complexity of the dynamical behavior of the system and its high sensitivity to the initial orientation of the shell and to the presence of any initial angular velocity normal to the surface. Full article
(This article belongs to the Special Issue Numerical Simulation of Nonlinear Dynamical Systems)
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17 pages, 3125 KiB  
Article
Network Characteristic Control of Social Dilemmas in a Public Good Game: Numerical Simulation of Agent-Based Nonlinear Dynamics
by Chulwook Park
Processes 2022, 10(7), 1348; https://doi.org/10.3390/pr10071348 - 11 Jul 2022
Viewed by 1217
Abstract
This paper proposes a possible mechanism for obtaining sizeable behavioral structures by simulating a network–agent dynamic on an evolutionary public good game with available social .learning. The model considers a population with a fixed number of players. In each round, the chosen players [...] Read more.
This paper proposes a possible mechanism for obtaining sizeable behavioral structures by simulating a network–agent dynamic on an evolutionary public good game with available social .learning. The model considers a population with a fixed number of players. In each round, the chosen players may contribute part of their value to a common pool. Then, each player may imitate the strategy of another player based on relative payoffs (whoever has the lower payoff adopts the strategy of the other player) and change his or her strategy using different exploratory variables. Relative payoffs are subject to incentives, including participation costs, but may also be subject to mutation, whose rate is sensitized by the network characteristics (social ties). The process discussed in this report is interesting and relevant across a broad range of disciplines that use game theory, including cultural evolutionary dynamics. Full article
(This article belongs to the Special Issue Numerical Simulation of Nonlinear Dynamical Systems)
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19 pages, 1740 KiB  
Article
Numerical Simulation Approach for a Dynamically Operated Sorption-Enhanced Water-Gas Shift Reactor
by Tabea J. Stadler, Jan-Hendrik Knoop, Simon Decker and Peter Pfeifer
Processes 2022, 10(6), 1160; https://doi.org/10.3390/pr10061160 - 9 Jun 2022
Cited by 3 | Viewed by 2181
Abstract
A dynamically operated sorption-enhanced water–gas shift reactor is modelled to leverage its performance by means of model-based process design. This reactor shall provide CO2-free synthesis gas for e-fuel production from pure CO. The nonlinear model equations describing simultaneous adsorption and reaction [...] Read more.
A dynamically operated sorption-enhanced water–gas shift reactor is modelled to leverage its performance by means of model-based process design. This reactor shall provide CO2-free synthesis gas for e-fuel production from pure CO. The nonlinear model equations describing simultaneous adsorption and reaction are solved with three numerical approaches in MATLAB: a built-in solver for partial differential equations, a semi-discretization method in combination with an ordinary differential equation solver, and an advanced graphic implementation of the latter method in Simulink. The novel implementation in Simulink offers various advantages for dynamic simulations and is expanded to a process model with six reaction chambers. The continuous conditions in the reaction chambers and the discrete states of the valves, which enable switching between reactive adsorption and regeneration, lead to a hybrid system. Controlling the discrete states in a finite-state machine in Stateflow enables automated switching between reactive adsorption and regeneration depending on predefined conditions, such as a time span or a concentration threshold in the product gas. The established chemical reactor simulation approach features unique possibilities in terms of simulation-driven development of operating procedures for intensified reactor operation. In a base case simulation, the sorbent usage for serial operation with adjusted switching times is increased by almost 15%. Full article
(This article belongs to the Special Issue Numerical Simulation of Nonlinear Dynamical Systems)
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12 pages, 3837 KiB  
Article
Analytical Routes to Chaos and Controlling Chaos in Brushless DC Motors
by Shun-Chang Chang
Processes 2022, 10(5), 814; https://doi.org/10.3390/pr10050814 - 21 Apr 2022
Viewed by 1541
Abstract
This study examines the dynamics in a brushless DC motor (BLDCM) and methods used to control potentially chaotic behavior or behavior similar to chaotic processes in these systems. Bifurcation diagrams revealed complex nonlinear behaviors over a range of parameter values. In the resulting [...] Read more.
This study examines the dynamics in a brushless DC motor (BLDCM) and methods used to control potentially chaotic behavior or behavior similar to chaotic processes in these systems. Bifurcation diagrams revealed complex nonlinear behaviors over a range of parameter values. In the resulting bifurcation diagram, period-doubling bifurcation, period-three bifurcation, and chaotic behavior can clearly be seen. We used Lyapunov exponents and Lyapunov dimensions to show the occurrence of chaos in a BLDCM. We then used the state feedback method to control chaos behaviors in the same BLDCM. Numerical simulations show the feasibility of the suggested means. Analysis of robustness against parametric perturbation in a BLDCM was performed from the perspective of Lyapunov stability theory and by using numerical simulations. We believe that studying the nonlinear dynamics and controlling chaos in BLDCMs will help to advance the development of high-performance electric vehicles. Full article
(This article belongs to the Special Issue Numerical Simulation of Nonlinear Dynamical Systems)
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28 pages, 12202 KiB  
Article
Influence of Nonlinear Dynamics Behavior of the Roller Follower on the Contact Stress of Polydyne Cam Profile
by Louay S. Yousuf
Processes 2022, 10(3), 585; https://doi.org/10.3390/pr10030585 - 17 Mar 2022
Cited by 4 | Viewed by 1659
Abstract
The effect of the cam profile on the nonlinear dynamics phenomenon of the follower is studied at three involutes’ profiles for the cam. The value of the Lyapunov exponent parameter is calculated at different internal distances of the follower guide from inside and [...] Read more.
The effect of the cam profile on the nonlinear dynamics phenomenon of the follower is studied at three involutes’ profiles for the cam. The value of the Lyapunov exponent parameter is calculated at different internal distances of the follower guide from inside and at different cam speeds. The effect of the Lyapunov exponent value on the contact stress is studied based on the clearance between the follower and its guides. The contact between the cam and the square grooving key and between the cam and the follower has been taken into consideration at different locations. The finite element method is used to calculate the contact stress numerically using the SolidWorks program. The nonlinear response of the follower is calculated analytically using the Newton–Euler equations of rigid body dynamics of translation and rotation motions while the follower position is tracked experimentally using a high-speed 3-D camera device. The contact stress is checked and verified using photo-elastic apparatus. The data of the contact stress against time are used in the Wolf algorithm code to extract the value of the largest Lyapunov exponent. A phase-plane diagram is drawn at different cam speeds and different internal distances of the follower guide from the inside. The periodic and non-periodic motions of the contact stress are examined at different contact locations for the follower with the cam profile. The higher the value of contact stress, the higher the value of the largest Lyapunov exponent parameter and the higher the value of bending deflection. Full article
(This article belongs to the Special Issue Numerical Simulation of Nonlinear Dynamical Systems)
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35 pages, 14313 KiB  
Article
Integral Resonant Controller to Suppress the Nonlinear Oscillations of a Two-Degree-of-Freedom Rotor Active Magnetic Bearing System
by Nasser A. Saeed, Mohamed S. Mohamed, Sayed K. Elagan and Jan Awrejcewicz
Processes 2022, 10(2), 271; https://doi.org/10.3390/pr10020271 - 29 Jan 2022
Cited by 11 | Viewed by 2162
Abstract
Within this article, the nonlinear vibration control of the rotor active magnetic bearings system is tackled utilizing the integral resonant controller for the first time. Two integral resonant controllers are proposed to mitigate the system lateral oscillations in the horizontal and vertical directions. [...] Read more.
Within this article, the nonlinear vibration control of the rotor active magnetic bearings system is tackled utilizing the integral resonant controller for the first time. Two integral resonant controllers are proposed to mitigate the system lateral oscillations in the horizontal and vertical directions. Based on the suggested control technique, the whole system dynamical model is derived as a two-degree-of-freedom nonlinear system (i.e., rotor system) coupled linearly to two first-order filters (i.e., the integral resonant controllers). The nonlinear autonomous system that governs the oscillation amplitudes of the controlled system as a function of the control parameters is extracted by applying perturbation analysis. The obtained autonomous system showed that the linear damping coefficients of the rotor system are functions of the control gains, feedback gains, and internal loop feedback gains of the coupled controller. Accordingly, the sensitivity of the rotor oscillation amplitudes to the different control parameters is explored. The stability margins and the optimal control gains are reported via plotting the different stability charts in two-dimensional space. The main acquired results demonstrated that the vibration suppression efficiency of the proposed controller is proportional to the product of both the control and feedback signal gains, and inversely proportional to the square of the internal loop feedback gains. In addition, the analytical investigations confirmed that the proposed integral resonant control method can force the rotor system to respond as a linear one with a single periodic attractor when the control parameters are designed properly. Finally, numerical simulations are performed that have illustrated the excellent correspondence with the obtained analytical results. Full article
(This article belongs to the Special Issue Numerical Simulation of Nonlinear Dynamical Systems)
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17 pages, 5401 KiB  
Article
Localizing Bifurcations in Non-Linear Dynamical Systems via Analytical and Numerical Methods
by Jan Kyzioł and Andrzej Okniński
Processes 2022, 10(1), 127; https://doi.org/10.3390/pr10010127 - 8 Jan 2022
Cited by 1 | Viewed by 1269
Abstract
In this paper, we study the bifurcations of non-linear dynamical systems. We continue to develop the analytical approach, permitting the prediction of the bifurcation of dynamics. Our approach is based on implicit (approximate) amplitude-frequency response equations of the form [...] Read more.
In this paper, we study the bifurcations of non-linear dynamical systems. We continue to develop the analytical approach, permitting the prediction of the bifurcation of dynamics. Our approach is based on implicit (approximate) amplitude-frequency response equations of the form FΩ,A;c̲ =0, where c̲ denotes the parameters. We demonstrate that tools of differential geometry make possible the discovery of the change of differential properties of solutions of the equation FΩ,A;c̲ =0. Such qualitative changes of the solutions of the amplitude-frequency response equation, referred to as metamorphoses, lead to qualitative changes of dynamics (bifurcations). We show that the analytical prediction of metamorphoses is of great help in numerical simulation. Full article
(This article belongs to the Special Issue Numerical Simulation of Nonlinear Dynamical Systems)
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14 pages, 2045 KiB  
Article
Research on the Approximate Calculation Method of the Fundamental Frequency and Its Characteristics on a Tensioned String Bridge
by Guangwei Zhou, Changzhao Qian and Changping Chen
Processes 2022, 10(1), 126; https://doi.org/10.3390/pr10010126 - 8 Jan 2022
Cited by 3 | Viewed by 1423
Abstract
As a new type of composite bridge, the dynamic structural characteristics of a tensioned string bridge need to be deeply studied. In this paper, based on the structural characteristics of a tensioned string bridge, the Rayleigh method is used to derive formulas for [...] Read more.
As a new type of composite bridge, the dynamic structural characteristics of a tensioned string bridge need to be deeply studied. In this paper, based on the structural characteristics of a tensioned string bridge, the Rayleigh method is used to derive formulas for calculating the frequencies of vertical, antisymmetric and lateral bending vibrations. The characteristics of the vertical and lateral bending vibration frequencies are summarized. The fundamental frequencies of the antisymmetric vertical bending and lateral bending of the tensioned string bridge are the same as that of the single-span beam under the corresponding constraint conditions. The shape and physical characteristics of the main cable have no effect on the frequency. The vertical bending symmetrical vibration frequency of the tensioned string bridge is greater than the corresponding symmetrical vibration frequency of the simply supported beam. The shape and physical characteristics of the main cable have a greater impact on the vertical bending symmetrical vibration frequency than the lateral bending frequency, and the vertical bending symmetrical vibration frequency increases with an increasing rise-to-span ratio. The tension force of the main cable has no influence on the frequency of tensioned string bridges. The first-order frequency of the tensioned string bridge is generally the vertical bending symmetrical vibration frequency. By adopting a tensioned string bridge structure, the fundamental frequency of a structure can be greatly increased, thereby increasing the overall rigidity of the structure. Finally, an engineering example is applied with the finite element parameter analysis method to study the vibration frequency characteristics of the tensioned string bridge, which verifies the correctness of the formula derived in this paper. The finite element analysis results show that the errors between the derived formula in this paper and the finite element calculation results are less than 2%, indicating that the formula derived in this paper has high calculation accuracy and can meet the calculation accuracy requirements of engineering applications. Full article
(This article belongs to the Special Issue Numerical Simulation of Nonlinear Dynamical Systems)
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18 pages, 5627 KiB  
Article
Research on Segmented Belt Acceleration Curve Based on Automated Mechanical Transmission
by Yunxia Li and Lei Li
Processes 2022, 10(1), 106; https://doi.org/10.3390/pr10010106 - 5 Jan 2022
Cited by 2 | Viewed by 2019
Abstract
An automated mechanical transmission (AMT) is proposed as a new soft starter for medium-scale belt conveyors in this paper. The AMT is used to start the belt conveyor and shift gears step by step to make the belt conveyor accelerate softly. Based on [...] Read more.
An automated mechanical transmission (AMT) is proposed as a new soft starter for medium-scale belt conveyors in this paper. The AMT is used to start the belt conveyor and shift gears step by step to make the belt conveyor accelerate softly. Based on analyzing common soft-starting acceleration curves, a segmented belt acceleration curve is proposed as a new soft-starting acceleration curve. By analyzing the AMT soft-starting system, the system modeling is built and the AMT output shaft’s angular acceleration is proposed to be controlled to control the belt acceleration. The AMT soft-starting simulation model is established in the environment of AMESim, and simulation results of the soft-starting process from the first to eighth gear positions are given. The main parameter curves of the AMT soft-starting system including the belt, driving pulley, and AMT output shaft are analyzed. The simulation model can indicate the viscoelastic property of the belt. The simulation results prove that the segmented belt acceleration is appropriate for a medium-scale belt conveyor and provide a theoretical and reasonable basis for using an AMT as a soft starter. Full article
(This article belongs to the Special Issue Numerical Simulation of Nonlinear Dynamical Systems)
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16 pages, 2473 KiB  
Article
Analysis of Dynamic Characteristics for Machine Tools Based on Dynamic Stiffness Sensitivity
by Chunhui Li, Zhiqiang Song, Xianghua Huang, Hui Zhao, Xuchu Jiang and Xinyong Mao
Processes 2021, 9(12), 2260; https://doi.org/10.3390/pr9122260 - 15 Dec 2021
Cited by 4 | Viewed by 3016
Abstract
Dynamic parameters are the intermediate information of the entirety of machine dynamics. The differences between components have not been combined with the structural vibration in the cutting process, so it is difficult to directly represent the dynamic characteristics of the whole machine related [...] Read more.
Dynamic parameters are the intermediate information of the entirety of machine dynamics. The differences between components have not been combined with the structural vibration in the cutting process, so it is difficult to directly represent the dynamic characteristics of the whole machine related to spatial position. This paper presents a method to identify sensitive parts according to the dynamic stiffness-sensitivity algorithm, which represents the dynamic characteristics of the whole machine tool. In this study, two experiments were carried out, the simulation verification experiment (dynamic experiment with variable stiffness) and modal analysis experiment (vibration test of five-axis gantry milling machine). The key modes of sensitive parts obtained by this method can represent the position-related dynamic characteristics of the whole machine. The characteristic obtained is that the inherent properties of machine-tool structure are independent of excitation. The method proposed in this paper can accurately represent the dynamic characteristics of the whole machine tool. Full article
(This article belongs to the Special Issue Numerical Simulation of Nonlinear Dynamical Systems)
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19 pages, 7520 KiB  
Article
Resonance Analysis and Vibration Reduction Optimization of Agricultural Machinery Frame—Taking Vegetable Precision Seeder as an Example
by Jinwu Wang, Changsu Xu, Yanan Xu, Jinfeng Wang, Wenqi Zhou, Qi Wang and Han Tang
Processes 2021, 9(11), 1979; https://doi.org/10.3390/pr9111979 - 5 Nov 2021
Cited by 6 | Viewed by 1847
Abstract
In order to solve the problem of vigorous vibration of agricultural machinery frames, taking a vegetable precision seeder as an example, the concept of vibration reduction was proposed. The modal analysis of the frame was carried out, and the accuracy of the finite [...] Read more.
In order to solve the problem of vigorous vibration of agricultural machinery frames, taking a vegetable precision seeder as an example, the concept of vibration reduction was proposed. The modal analysis of the frame was carried out, and the accuracy of the finite element model was verified by comparing the modal test of multipoint input and multipoint output (MIMO) and simulation results. Additionally, the main frequency of engine vibration was the main excitation source of frame resonance. According to the modal shapes, it was proposed to increase the fixed beam structure and to carry out simulation tests. The time-domain signal of the maximum deformation position in the first-order vibration mode was measured, and the vibration spectrum analysis maps before and after optimization were obtained by Fourier transform. A field experiment showed that the seeding quality of the whole machine was significantly improved after optimization. This study provides a reference for the analysis of vibration characteristics and the vibration reduction design of the agricultural machinery equipment. Full article
(This article belongs to the Special Issue Numerical Simulation of Nonlinear Dynamical Systems)
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16 pages, 4743 KiB  
Article
Chaotic Analysis and Prediction of Wind Speed Based on Wavelet Decomposition
by Li Lin, Dandan Xia, Liming Dai, Qingsong Zheng and Zhiqin Qin
Processes 2021, 9(10), 1793; https://doi.org/10.3390/pr9101793 - 10 Oct 2021
Cited by 4 | Viewed by 1588
Abstract
Studying the characteristics of wind speed is essential in wind speed prediction. Based on long-term observed wind speed data, fractal dimension analysis of wind speed was first conducted at different scales, and persistence in wind speed was evaluated based on fractal dimensions in [...] Read more.
Studying the characteristics of wind speed is essential in wind speed prediction. Based on long-term observed wind speed data, fractal dimension analysis of wind speed was first conducted at different scales, and persistence in wind speed was evaluated based on fractal dimensions in this paper. To propose a more accurate model for wind speed prediction, the wavelet decomposition method was applied to separate the high-frequency dynamics of wind speed data from the low-frequency dynamics. Chaotic behaviors were studied for each decomposed component using the largest Lyapunov exponents method. A proposed hybrid prediction method combining wavelet decomposition, a chaotic prediction method and a Kalman filter method was investigated for short-term wind speed prediction. Simulation results showed that the proposed method can significantly improve prediction accuracy. Full article
(This article belongs to the Special Issue Numerical Simulation of Nonlinear Dynamical Systems)
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