scholarly journals Study on Rub-Impact Dynamical Behavior of An Asymmetrical Rotor-Bearing with Variable Ratio of Stiffness

2015 ◽  
Vol 9 (1) ◽  
pp. 80-85
Author(s):  
Tan Lian ◽  
Dang Pei
Keyword(s):  
Dynamical Behavior ◽  
Mathematic Model ◽  
Variable Ratio ◽  
Bifurcation Diagrams ◽  
Low Frequencies ◽  
Generating Sets ◽  
Rotor Bearing ◽  
Exact Identification ◽  
Rotor Stiffness ◽  
Safety Operation

A rub-impact mathematic model of an Asymmetrical rotor-bearing with nonlinear oil film force is built in the paper. The bifurcation diagrams of the response were given following the changing of ratio of stiffness. We analyzed the bifurcation and the chaos character of an Asymmetrical rotor-bearing with operating rotor stiffness changing, then we get the dynamical character and the law when the rubbing happen. The nonlinear dynamic behaviors of the system were studied by using the numerical value integral and Poincare mapping methods. By analysis the process of rub-impact, it is so complex and many low frequencies with large amplitude are in the range of 0.3~0.6 X. The way of period-chaos-period and the phenomena of diverging backward whirl are discovered when the rubbing happen. These results provide important theoretical references for the safety operation of generating sets and the exact identification of the faults in rotating machinery.

scholarly journals Fear effect in discrete prey-predator model incorporating square root functional response

2021 ◽  
Vol 2 (2) ◽  
pp. 51-57
Author(s):  
P.K. Santra
Keyword(s):  
Functional Response ◽  
Stability Condition ◽  
Discrete Model ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Square Root ◽  
Bifurcation Diagrams ◽  
Fear Effect ◽  
Hypothetical Data ◽  
Predator Model

In this work, an interaction between prey and its predator involving the effect of fear in presence of the predator and the square root functional response is investigated. Fixed points and their stability condition are calculated. The conditions for the occurrence of some phenomena namely Neimark-Sacker, Flip, and Fold bifurcations are given. Base on some hypothetical data, the numerical simulations consist of phase portraits and bifurcation diagrams are demonstrated to picturise the dynamical behavior. It is also shown numerically that rich dynamics are obtained by the discrete model as the effect of fear.

Study on Derailment Mechanism and Safety Operation Area of High-Speed Trains Under Earthquake

2012 ◽  
Vol 7 (4) ◽  
Author(s):  
Liang Ling ◽  
Xinbiao Xiao ◽  
Xuesong Jin
Keyword(s):  
High Speed ◽  
Dynamical Behavior ◽  
Vehicle Speed ◽  
Vertical Force ◽  
Explicit Integration ◽  
Running Safety ◽  
Earthquake Motion ◽  
High Speed Trains ◽  
Wheel Loading ◽  
Safety Operation

In order to investigate the derailment mechanism and safety operation area of high-speed trains under earthquake, a coupled vehicle-track dynamic model considering earthquake effect is developed, in which the vehicle is modeled as a 35 degrees of freedom (DOF) multibody system with nonlinear suspension characteristic and the slab track is modeled as a discrete elastic support model. The rails of the track are assumed to be Timoshenko beams supported by discrete rail fasteners, and the slabs are modeled with solid finite elements. The system motion equations are solved by means of an explicit integration method in time domain. The present work analyzes in detail the effect of earthquake characteristics on the dynamical behaviors of a vehicle-track coupling system and the transient derailment criteria. The considered derailment criteria include the ratio of the wheel/rail lateral force to the vertical force, the wheel loading reduction, the wheel/rail contact point traces on the wheel tread, and the wheel rise with respect to the rail top, respectively. The present work also finds the safety operation area, the derailment area, and the warning area of high-speed trains under earthquake, and their boundaries. These areas consist of three key parameters influencing the dynamical behavior of high-speed train and track under earthquake. The three key influencing parameters are, respectively, the vehicle speed and the lateral and vertical peak ground acceleration (PGA) of an earthquake. The results obtained indicate that the lateral earthquake motion has a greater influence on the vehicle dynamic behavior and its running safety compared to the vertical earthquake motion. The risk of derailment increases quickly with the increasing of lateral earthquake motion amplitude. The lateral earthquake motion is dominant in the vehicle running safety influenced by an earthquake. While the vertical earthquake motion promotes jumping of the wheels easily, not easy is flange climb derailment. And the effect of the vehicle speed is not significant under earthquake.

Seismic Response Analysis on a Chaotic System

2013 ◽  
Vol 639-640 ◽  
pp. 911-916
Author(s):  
Cui Xiang Liang
Keyword(s):  
Seismic Response ◽  
Chaotic System ◽  
Center Manifold ◽  
Dynamical Behavior ◽  
Response Analysis ◽  
Bifurcation Diagrams ◽  
Seismic Response Analysis ◽  
Nonlinear Seismic Response ◽  
Hyperbolic Equilibrium ◽  
Hyperbolic Equilibrium Point

This paper is concerned with the dynamical behavior of a chaotic system which is a model for seismic response of structures. The local bifurcation of the non-hyperbolic equilibrium point of the chaotic system is investigated by using center manifold method. The transcritical bifurcation is analyzed in detail. Based on numerical simulations, spectrums of maximal Lyapunov exponent and the bifurcation diagrams are presented for the dynamic analysis. The method proposed can be used as a reference of nonlinear seismic response analysis.

Research on Mathematic Model and Measuring Method of Moving Beam Attitude in Large Forging Hydraulic Press

2011 ◽  
Vol 128-129 ◽  
pp. 1213-1216
Author(s):  
Hui Chen ◽  
Jian Ping Tan ◽  
Jin Li Gong ◽  
Xian Yue Cao ◽  
Ji Neng Zhou
Keyword(s):  
Research Result ◽  
Mathematic Model ◽  
Measuring Method ◽  
Hydraulic Press ◽  
Large Forging ◽  
Mechanical Feature ◽  
Object A ◽  
Moving Beam ◽  
Safety Operation ◽  
Special Working

The moving beam of large forging hydraulic press is taken as a research object. A mathematic model of moving beam’s six freedom degrees attitude is established. According to the mechanical feature and special working conditions of large forging hydraulic press, a non-contacted method for moving beam attitude measuring which based on machine vision is proposed. The basic principle and composition of the system are introduced. The system is applied in 300MN large forging hydraulic press, and large amounts of monitoring data are collected which confirm that the measuring method is effective. The research result is helpful for the safety operation and maintenance of large forging hydraulic press.

scholarly journals EFFECTS OF TREATMENT, AWARENESS AND CONDOM USE IN A COINFECTION MODEL FOR HIV AND HCV IN MSM

2015 ◽  
Vol 23 (02) ◽  
pp. 165-193 ◽  
Author(s):  
CARLA M. A. PINTO ◽  
ANA CARVALHO
Keyword(s):  
Human Immunodeficiency Virus ◽  
Hepatitis C Virus ◽  
Hepatitis C ◽  
Local Stability ◽  
Dynamical Behavior ◽  
Full Model ◽  
Bifurcation Diagrams ◽  
Immunodeficiency Virus ◽  
Disease Free ◽  
Qualitative Changes

We develop a new a coinfection model for hepatitis C virus (HCV) and the human immunodeficiency virus (HIV). We consider treatment for both diseases, screening, unawareness and awareness of HIV infection, and the use of condoms. We study the local stability of the disease-free equilibria for the full model and for the two submodels (HCV only and HIV only submodels). We sketch bifurcation diagrams for different parameters, such as the probabilities that a contact will result in a HIV or an HCV infection. We present numerical simulations of the full model where the HIV, HCV and double endemic equilibria can be observed. We also show numerically the qualitative changes of the dynamical behavior of the full model for variation of relevant parameters. We extrapolate the results from the model for actual measures that could be implemented in order to reduce the number of infected individuals.

scholarly journals Bifurcation Diagrams and Global Phase Portraits for Some Hamiltonian Systems with Rational Potentials

2018 ◽  
Vol 28 (13) ◽  
pp. 1850168
Author(s):  
Ting Chen ◽  
Jaume Llibre
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Normal Forms ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Linear Change ◽  
Rational Potential ◽  
Change Of Variables ◽  
Poincaré Disk

In this paper, we study the global dynamical behavior of the Hamiltonian system [Formula: see text], [Formula: see text] with the rational potential Hamiltonian [Formula: see text], where [Formula: see text] and [Formula: see text] are polynomials of degree 1 or 2. First we get the normal forms for these rational Hamiltonian systems by some linear change of variables. Then we classify all the global phase portraits of these systems in the Poincaré disk and provide their bifurcation diagrams.

scholarly journals Nonlinear Dynamic Characteristics of Marine Rotor-Bearing System under Heaving Motion

2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Yongchao Han ◽  
Ming Li
Keyword(s):  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Dynamic Performance ◽  
Chaotic Oscillation ◽  
Mathematic Model ◽  
Rotating Speed ◽  
Period 2 ◽  
Rotor Bearing ◽  
Motion Period ◽  
Bearing System

In this paper, the influence of the heaving motion on the nonlinear dynamic behavior of the rotor-bearing system is considered. First, a mathematic model of the marine rotor-bearing system is developed on the short bearing theory in the noninertial reference system, in which the heaving motion is taken into account. Then its dynamic characteristics are analyzed based on the numerical integration method, such as the bifurcation diagram, the largest Lyapunov exponents (LLE), the steady-state response, and the rotor orbit and its Poincaré map. The results indicate that heaving motion has a great effect on the dynamics of the rotor system, which exhibits a period 1 motion at low rotating speed, with the increase of the rotating speed, the phenomena of the quasiperiodic, period 2, and double Hopf bifurcations appear. Its dynamic performance presents a period 1 motion, period 2, quasiperiodic, and chaotic oscillation.

Water Hammer Characteristics of Glass Reinforced Plastic Oil Transportation Pipeline

2011 ◽  
Vol 204-210 ◽  
pp. 127-130 ◽  
Author(s):  
Chang Jun Li ◽  
Xia Wu ◽  
Wen Long Jia ◽  
Ke Xi Liao
Keyword(s):  
Pressure Fluctuation ◽  
Peak Pressure ◽  
Mathematic Model ◽  
Water Hammer ◽  
Steel Pipeline ◽  
Oil Transportation ◽  
Reinforced Plastic ◽  
Fluctuation Frequency ◽  
Simulation Results ◽  
Safety Operation

Glass reinforced plastic (GRP) pipeline has good characteristics of anti-corrosion, anti-scaling and it is widely used in the oil transportation pipeline. Analyze the water hammer characteristics of GRP pipeline is essential to ensure the safety operation of the pipeline. The water hammer mathematic model for GRP pipeline is built through combing the general water hammer mathematic model and prosperities of GRP pipeline. The solving method of the model is discussed based on the method of characteristic. Ultimately, the simulation results show the GRP pipeline can reduce the peak pressure and pressure fluctuation frequency as well as increase the low pressure caused by water hammer compared with steel pipeline. The GRP pipeline has a better capability to reduce the harms brought by water hammer than steel pipeline.

Dynamics of a Rolling Wheelset

1993 ◽  
Vol 46 (7) ◽  
pp. 438-444 ◽  
Author(s):  
Hans True
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Chaotic Motion ◽  
Dynamical Behavior ◽  
Railway Track ◽  
Kinematics And Dynamics ◽  
Bifurcation Diagrams ◽  
Speed Range ◽  
Set Up ◽  
The Mathematical Model

We discuss the kinematics and dynamics of a wheelset rolling on a railway track. The mathematical model of a suspended wheelset rolling with constant speed on a straight track is set up and its dynamics is investigated numerically. The results are presented mainly on bifurcation diagrams. Several kinds of dynamical behavior is identified within the investigated speed range. We find a stationary equilibrium point at low speeds and at higher speeds symmetric and asymmetric oscillations are found and ranges with chaotic motion are identified. The bifurcations are described.

Numerical study of a rotor-bearing-seal system

2007 ◽  
Vol 221 (7) ◽  
pp. 779-788 ◽  
Author(s):  
M Cheng ◽  
G Meng ◽  
J P Jing
Keyword(s):  
Periodic Motion ◽  
Numerical Study ◽  
Coupled System ◽  
Bifurcation Diagrams ◽  
Frequency Spectra ◽  
Linear Dynamic ◽  
Non Linear ◽  
Rotor Bearing ◽  
Largest Lyapunov Exponents ◽  
Bearing Characteristic

Seal and bearing characteristic is an important factor affecting the performance of the rotor system. The non-linear dynamic behaviours of a rotor-bearing-seal coupled system are investigated. Dynamic trajectories, Poincaré maps, largest Lyapunov exponents, frequency spectra, and bifurcation diagrams which are applied to analyse the features of the rotor-bearing-seal system in various parameters. Various non-linear phenomena in the rotor-bearing-seal system, such as periodic motion, double-periodic motion, multi-periodic, and quasi-periodic motion are investigated. The results of this study may contribute to a further understanding of the non-linear dynamics of such a rotor-bearing-seal coupled system.

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