Dynamic Mechanism of a Train Suspension System

2010 ◽  
Author(s):  
Albert C. J. Luo ◽  
Dennis O’Connor
Keyword(s):  
Numerical Simulations ◽  
System Parameter ◽  
Suspension System ◽  
Dynamic Mechanism ◽  
Impact Model ◽  
Periodic Motions ◽  
Chaotic Motions ◽  
Nonlinear Dynamical ◽  
Dynamical Behaviors ◽  
Mapping Structures

Nonlinear dynamical behaviors of a train suspension system with impacts are investigated. The suspension system is modelled through an impact model with possible stick between a bolster and two wedges. Based on the mapping structures, periodic motions of such a system are described. To understand the global dynamical behaviors of the train suspension system, system parameter maps are developed. Numerical simulations for periodic and chaotic motions are performed from the parameter maps.

Analytical Dynamics of Complex Motions in a Train Suspension System

2011 ◽  
Author(s):  
Albert C. J. Luo ◽  
Dennis O’Conner
Keyword(s):  
Numerical Simulations ◽  
Suspension System ◽  
Analytical Prediction ◽  
Impact Model ◽  
Analytical Dynamics ◽  
Complex Motion ◽  
Chaotic Motions ◽  
Nonlinear Dynamical ◽  
Dynamical Behaviors ◽  
Mapping Structures

Nonlinear dynamical behaviors of a train suspension system with impacts are investigated. The suspension system is described through an impact model with possible stick between a bolster and two wedges. The analytical conditions that reflect the motion mechanisms for the complex motion are given. The mapping structures for periodic and chaotic motions of such a system can be described. The analytical prediction of the complex motions can be conducted from the mapping structure, and numerical simulations for periodic and chaotic motions can be carried out in sequel.

Analytical Dynamics of a Ball Bouncing on a Vibrating Table

2012 ◽  
Author(s):  
Yu Guo ◽  
Albert C. J. Luo
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Analytical Dynamics ◽  
Periodic Motions ◽  
Chaotic Motions ◽  
Theory Of Flow ◽  
Mapping Structures ◽  
Ball Bouncing ◽  
Vibrating Table

In this paper, the theory of flow switchability for discontinuous dynamical systems is applied. Domains and boundaries for such a discontinuous problem are defined and analytical conditions for motion switching are developed. The conditions explain the important role of switching phase on the motion switchability in such a system. To describe different motions, the generic mappings and mapping structures are introduced. Bifurcation scenarios for periodic and chaotic motions are presented for different motions and switchability. Numerical simulations are provided for periodic motions with impacts only and with impact chatter to stick in the system.

scholarly journals Motion Switching and Chaos of a Particle in a Generalized Fermi-Acceleration Oscillator

2009 ◽  
Vol 2009 ◽  
pp. 1-40 ◽  
Author(s):  
A. C. J. Luo ◽  
Y. Guo
Keyword(s):  
Local Stability ◽  
Analytical Prediction ◽  
Fermi Acceleration ◽  
Periodic Motions ◽  
Chaotic Motions ◽  
Dynamical Behaviors ◽  
Global View ◽  
Mapping Structures ◽  
Stability And Bifurcations ◽  
First Time

Dynamic behaviors of a particle (or a bouncing ball) in a generalized Fermi-acceleration oscillator are investigated. The motion switching of a particle in the Fermi-oscillator causes the complexity and unpredictability of motion. Thus, the mechanism of motion switching of a particle in such a generalized Fermi-oscillator is studied through the theory of discontinuous dynamical systems, and the corresponding analytical conditions for the motion switching are developed. From solutions of linear systems in subdomains, four generic mappings are introduced, and mapping structures for periodic motions can be constructed. Thus, periodic motions in the Fermi-acceleration oscillator are predicted analytically, and the corresponding local stability and bifurcations are also discussed. From the analytical prediction, parameter maps of periodic and chaotic motions are achieved for a global view of motion behaviors in the Fermi-acceleration oscillator. Numerical simulations are carried out for illustrations of periodic and chaotic motions in such an oscillator. In existing results, motion switching in the Fermi-acceleration oscillator is not considered. The motion switching for many motion states of the Fermi-acceleration oscillator is presented for the first time. This methodology will provide a useful way to determine dynamical behaviors in the Fermi-acceleration oscillator.

Periodic Motions in an Autonomous System With a Discontinuous Vector Field

2020 ◽  
Author(s):  
Siyu Guo ◽  
Albert C. J. Luo
Keyword(s):  
Vector Field ◽  
Dynamical Systems ◽  
Numerical Simulations ◽  
Autonomous System ◽  
Parameter Study ◽  
Spring Stiffness ◽  
Algebraic Equations ◽  
Periodic Motions ◽  
Mapping Structures ◽  
The Stability

Abstract In this paper, periodic motions in an autonomous system with a discontinuous vector field are discussed. The periodic motions are obtained by constructing a set of algebraic equations based on motion mapping structures. The stability of periodic motions is investigated through eigenvalue analysis. The grazing bifurcations are presented by varying the spring stiffness. Once the grazing bifurcation occurs, periodic motions switches from the old motion to a new one. Numerical simulations are conducted for motion illustrations. The parameter study helps one understand autonomous discontinuous dynamical systems.

Dynamics of a Simplified van der Pol Oscillator Revisited

2007 ◽  
Author(s):  
Albert C. J. Luo ◽  
Arun Rajendran
Keyword(s):  
Bifurcation Analysis ◽  
Local Stability ◽  
Van Der Pol Oscillator ◽  
Nonsmooth Dynamics ◽  
Mapping Technique ◽  
Periodic Motions ◽  
Van Der Pol ◽  
Chaotic Motions ◽  
Mapping Structures ◽  
Stability And Bifurcation Analysis

In this paper, the dynamic characteristics of a simplified van der Pol oscillator are investigated. From the theory of nonsmooth dynamics, the structures of periodic and chaotic motions for such an oscillator are developed via the mapping technique. The periodic motions with a certain mapping structures are predicted analytically for m-cycles with n-periods. Local stability and bifurcation analysis for such motions are carried out. The (m:n)-periodic motions are illustrated. The further investigation of the stable and unstable periodic motions in such a system should be completed. The chaotic motion based on the Levinson donuts should be further discussed.

Periodic Motions of a Semi-Active Suspension System With MR Damping.

2006 ◽  
Author(s):  
Albert C. J. Luo ◽  
Arun Rajendran
Keyword(s):  
Piecewise Linear ◽  
Active Suspension ◽  
Suspension System ◽  
Mapping Technique ◽  
Periodic Motions ◽  
Mapping Structures ◽  
The Stability ◽  
Magneto Rheological ◽  
Mr Damping ◽  
Full Nonlinearity

Periodic motions in a hysteretically damped, semi-active suspension system are investigated. The Magneto-Rheological damping varying with relative velocity is modeled through a piecewise-linear model. The theory for discontinuous dynamical systems is employed to determine the grazing motions in such a system, and the mapping technique is used to develop the mapping structures of periodic motions. The periodic motions are predicted analytically and verified numerically. The stability and bifurcation analyses of such periodic motions are performed, and the parameters for all possible motions are developed. This model is applicable for the semi-active suspension system with the Magneto-Rheological damper in automobiles. The further investigation on the Magneto-Rheological damping with full nonlinearity should be completed.

On Symmetric Periodic Motions With Different Excitation Periods in a Discontinuous System With a Hyperbolic Boundary

2020 ◽  
Author(s):  
Albert C. J. Luo ◽  
Chuanping Liu
Keyword(s):  
Dynamic System ◽  
Numerical Simulations ◽  
Periodic Motions ◽  
Discontinuous System ◽  
Mapping Structures ◽  
Specific Mapping ◽  
Hyperbolic Boundary

Abstract In this paper, symmetric periodic motions with different excitation periods in a discontinuous dynamic system with a hyperbolic boundary are presented analytically. The switchability conditions of flows at the hyperbolic boundaries are developed. Periodic motions with specific mapping structures are predicted analytically, and numerical simulations of periodic motions are carried out. The corresponding G-functions are presented for illustration of motion switchability at the hyperbolic boundaries.

Period-1 Motions to Chaos in a Parametrically Excited Pendulum

2017 ◽  
Author(s):  
Yu Guo ◽  
Albert C. J. Luo
Keyword(s):  
Numerical Methods ◽  
Numerical Simulations ◽  
Bifurcation Analysis ◽  
Periodic Motions ◽  
Parametrically Excited ◽  
Pendulum System ◽  
Discrete Maps ◽  
Mapping Structures ◽  
Stability And Bifurcation Analysis ◽  
Simulation Results

In this paper, bifurcation trees of period-1 motions to chaos are investigated in a parametrically excited pendulum. To construct discrete mapping structures of periodic motions, implicit discrete maps are developed for such a pendulum system. The bifurcation trees from period-1 motions to chaos are predicted semi-analytically through period-1 to period-4 motions. The corresponding stability and bifurcation analysis are carried out through eigenvalue analysis. Finally, numerical simulations of periodic motions can be completed through numerical methods. Such simulation results are illustrated for verification of the analytical predictions.

Nonlinear Dynamics of a Gear Transmission System: Part I — Mechanism of Impacting Chatter With Stick

2007 ◽  
Author(s):  
Albert C. J. Luo ◽  
Dennis O’Connor
Keyword(s):  
Transmission System ◽  
Gear Transmission ◽  
Impact Model ◽  
Transmission Systems ◽  
Motion Mechanism ◽  
Nonlinear Dynamical ◽  
Dynamical Behaviors ◽  
Gear Transmission System ◽  
System Part ◽  
Nonlinear Behaviors

In this paper, an investigation on nonlinear dynamical behaviors of a transmission system with a gear pair is conducted. The transmission system is described through an impact model with possible stick between the two gears. From the theory of discontinuous dynamical systems, the motion mechanism of impacting chatter with stick is investigated. The onset and vanishing conditions of stick motions are developed, and the condition for maintaining the stick motion is achieved as well. The corresponding physics interpretation is given for a better understanding of nonlinear behaviors of gear transmission systems. Furthermore, such an understanding may be very helpful to improve the efficiency of gear transmission systems.

Periodic Motions in a Discontinuous Dynamical System With Two Circular Boundaries

2019 ◽  
Author(s):  
Siyu Guo ◽  
Albert C. J. Luo
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Numerical Simulations ◽  
Periodic Motions ◽  
Discontinuous Dynamical System ◽  
Mapping Structures

Abstract In this paper, periodic motions in a discontinuous dynamical systems are studied. The discontinuous dynamical system has three domains partitioned through two circular boundaries. On the three domains, there are three distinct dynamical systems. From the G-functions, the switchability conditions of a flow from one domain to anther domain at the boundary are developed. The flow mappings from a boundary to a bounbary are developed for each domain and boundary. From the mapping structures, periodic motions in the discontinuous dynamical system are predicted. Numerical simulations of periodic motions and motion switchability at boundaries are presented in the discontinuous dynamical system.

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