scholarly journals The Identification of Nonlinear Systems UsingCt-KtPlane Coordinates

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Ming-Fei Chen ◽  
Dyi-Cheng Chen ◽  
Chung-Heng Yang ◽  
Shih-Feng Tseng
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Dynamic Behavior ◽  
Pulse Response ◽  
Displacement Velocity ◽  
Viscous Damping ◽  
Dynamic Parameters ◽  
Coordinate Plane ◽  
Aerostatic Bearing ◽  
System A

In order to instantaneously distinguish theCt(coefficient of viscous damping) andKt(coefficient of stiffness), which are both functions of time in an M.C.K. nonlinear system, a new identification method is proposed in this paper. The graphs of theCt-Ktare analyzed and the dynamic behavior of M.C.K. systems in aCt-Ktcoordinate plane is discussed. This method calculates two adjacent sampling data, the displacement, velocity, and acceleration (which are obtained from the responses of a pulse response experiment) and then distinguishesCtandKtof an instantaneous system. Finally, this method is used to identify the aerostatic bearing dynamic parameters,CandK.

The Effect of Spring Mass on Nonlinear System Dynamic Behavior

2012 ◽  
Vol 197 ◽  
pp. 120-123
Author(s):  
Qing Chao Yang ◽  
Jing Jun Lou ◽  
Hai Ping Wu ◽  
Si Mi Tang
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Dynamic Behavior ◽  
Phase Plane ◽  
Dead Zone ◽  
Great Influence ◽  
System Dynamic ◽  
Motion Trajectories ◽  
Mass Spring ◽  
The Impact

A model is established in this paper about the impact of mass spring on the particle in nonlinear systems with dead-zone and the particle’s subsequent synchronised movement with spring. Simulates are conducted under different conditions, and it is found that when the spring mass is large, the phase plane of particle’s motion trajectories change significantly to the condition when spring is no mass. It is concluded that the spring mass have a great influence on the dynamic behavior of nonlinear systems with dead-zone.

scholarly journals A Note on Practical Stability of Nonlinear Vibration Systems with Impulsive Effects

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Qishui Zhong ◽  
Hongcai Li ◽  
Hui Liu ◽  
Juebang Yu
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Nonlinear Vibration ◽  
Stability Criterion ◽  
Fuzzy Model ◽  
Vibration Characteristics ◽  
Impulsive Effects ◽  
Practical Stability ◽  
Impulsive Systems ◽  
System A

This paper addresses the issue of vibration characteristics of nonlinear systems with impulsive effects. By utilizing a T-S fuzzy model to represent a nonlinear system, a general strict practical stability criterion is derived for nonlinear impulsive systems.

scholarly journals COMPUTER MODELING OF NONLINEAR SYSTEM VIBRATIONS WITH APPLOWANCE FOR NONLOCAL DAMPING

2018 ◽  
Vol 14 (1) ◽  
pp. 137-144
Author(s):  
Vadim V. Potapov ◽  
Elena S. Shepitko
Keyword(s):  
Problem Solving ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Galerkin Method ◽  
Computer Modeling ◽  
Dynamic Behavior ◽  
Forced Vibrations ◽  
The Galerkin Method

The paper is devoted to the analysis of the nonlocal damping consideration influence on the results of computer modeling of nonlinear systems subjected to periodic deterministic and stochastic stationary loads forced vibrations The shallow arc dynamic behavior is examined. The Galerkin method is used for the problem solving

A Controller Design for a Class of Nonlinear Systems Using the Lyapunov-Bellman Approach

1992 ◽  
Vol 114 (3) ◽  
pp. 390-393 ◽  
Author(s):  
R. T. Yanushevsky
Keyword(s):  
Optimal Control ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Optimal Control Problem ◽  
Lyapunov Functions ◽  
Bellman Equation ◽  
Controller Design ◽  
Variable Structure ◽  
System A

The method of synthesis for a wide class of nonlinear systems affine in control is considered. The proposed approach is based on the solution of a special optimal control problem. The integrand of the optimized functional is chosen in such a way that the Bellman equation has a desired solution. The nonlinear system design is reduced to the examination of the integrand of the optimized functional. To extend the domain of asymptotic stability of the nonlinear system, a sequence of the Lyapunov functions is used. The whole system becomes a system with variable structure.

Exact Stationary Response Solution for Second Order Nonlinear Systems Under Parametric and External White Noise Excitations: Part II

1988 ◽  
Vol 55 (3) ◽  
pp. 702-705 ◽  
Author(s):  
Y. K. Lin ◽  
Guoqiang Cai
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Probability Distribution ◽  
White Noise ◽  
Probability Density ◽  
Detailed Balance ◽  
Stationary Probability ◽  
Probability Flow ◽  
Parametric And External Excitations ◽  
White Noises

A systematic procedure is developed to obtain the stationary probability density for the response of a nonlinear system under parametric and external excitations of Gaussian white noises. The procedure is devised by separating the circulatory portion of the probability flow from the noncirculatory flow, thus obtaining two sets of equations that must be satisfied by the probability potential. It is shown that these equations are identical to two of the conditions established previously under the assumption of detailed balance; therefore, one remaining condition for detailed balance is superfluous. Three examples are given for illustration, one of which is capable of exhibiting limit cycle and bifurcation behaviors, while another is selected to show that two different systems under two differents sets of excitations may result in the same probability distribution for their responses.

scholarly journals Online Health Management for Complex Nonlinear Systems Based on Hidden Semi-Markov Model Using Sequential Monte Carlo Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-22
Author(s):  
Qinming Liu ◽  
Ming Dong
Keyword(s):  
Monte Carlo ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Markov Model ◽  
Sequential Monte Carlo ◽  
Health Management ◽  
Health State ◽  
Health States ◽  
Complex Nonlinear System ◽  
Complex Nonlinear Systems

Health management for a complex nonlinear system is becoming more important for condition-based maintenance and minimizing the related risks and costs over its entire life. However, a complex nonlinear system often operates under dynamically operational and environmental conditions, and it subjects to high levels of uncertainty and unpredictability so that effective methods for online health management are still few now. This paper combines hidden semi-Markov model (HSMM) with sequential Monte Carlo (SMC) methods. HSMM is used to obtain the transition probabilities among health states and health state durations of a complex nonlinear system, while the SMC method is adopted to decrease the computational and space complexity, and describe the probability relationships between multiple health states and monitored observations of a complex nonlinear system. This paper proposes a novel method of multisteps ahead health recognition based on joint probability distribution for health management of a complex nonlinear system. Moreover, a new online health prognostic method is developed. A real case study is used to demonstrate the implementation and potential applications of the proposed methods for online health management of complex nonlinear systems.

scholarly journals Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 854
Author(s):  
Raquel S. Rodríguez ◽  
Gilberto Gonzalez Avalos ◽  
Noe Barrera Gallegos ◽  
Gerardo Ayala-Jaimes ◽  
Aaron Padilla Garcia
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Nonlinear Dynamic ◽  
Bond Graph ◽  
Physical Domain ◽  
Graph Models ◽  
Simple Task ◽  
Analysis And Synthesis ◽  
Simulation Results

An alternative method to analyze a class of nonlinear systems in a bond graph approach is proposed. It is well known that the analysis and synthesis of nonlinear systems is not a simple task. Hence, a first step can be to linearize this nonlinear system on an operation point. A methodology to obtain linearization for consecutive points along a trajectory in the physical domain is proposed. This type of linearization determines a group of linearized systems, which is an approximation close enough to original nonlinear dynamic and in this paper is called dynamic linearization. Dynamic linearization through a lemma and a procedure is established. Therefore, linearized bond graph models can be considered symmetric with respect to nonlinear system models. The proposed methodology is applied to a DC motor as a case study. In order to show the effectiveness of the dynamic linearization, simulation results are shown.

scholarly journals Time-Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves

2003 ◽  
Vol 125 (2) ◽  
pp. 170-177 ◽  
Author(s):  
Lili Wang ◽  
Jinghui Zhang ◽  
Chao Wang ◽  
Shiyue Hu
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Linear Model ◽  
Frequency Analysis ◽  
Nonlinear Behavior ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Vibration Data ◽  
Identification Technique ◽  
Stiffness And Damping

The joint time-frequency analysis method is adopted to study the nonlinear behavior varying with the instantaneous response for a class of S.D.O.F nonlinear system. A time-frequency masking operator, together with the conception of effective time-frequency region of the asymptotic signal are defined here. Based on these mathematical foundations, a so-called skeleton linear model (SLM) is constructed which has similar nonlinear characteristics with the nonlinear system. Two skeleton curves are deduced which can indicate the stiffness and damping in the nonlinear system. The relationship between the SLM and the nonlinear system, both parameters and solutions, is clarified. Based on this work a new identification technique of nonlinear systems using the nonstationary vibration data will be proposed through time-frequency filtering technique and wavelet transform in the following paper.

Nonlinear Dynamic Behavior of a Rotor Bearing System With Nonlinear Viscous Damping Suspension

2017 ◽  
Author(s):  
Shuai Yan ◽  
Bin Lin ◽  
Jixiong Fei ◽  
Pengfei Liu
Keyword(s):  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
Vibration Isolation ◽  
Lubricating Oil ◽  
Viscous Damping ◽  
Oil Viscosity ◽  
Speed Range ◽  
Rotor Bearing ◽  
Nonlinear Dynamic Behavior ◽  
Bearing System

Nonlinear damping suspension has gained attention owing to its excellent vibration isolation performance. In this paper, a cubic nonlinear viscous damping suspension was introduced to a rotor bearing system for vibration isolation between the bearing and environment. The nonlinear dynamic response of the rotor bearing system was investigated thoroughly. First, the nonlinear oil film force was solved based short bearing approximation and half Sommerfeld boundary condition. Then the motion equations of the system was built considering the cubic nonlinear viscous damping. A computational method was used to solve the equations of motion, and the bifurcation diagrams were used to display the motions. The influences of rotor-bearing system parameters were discussed from the results of numerical calculation, including the eccentricity, mass, stiffness, damping and lubricating oil viscosity. The results showed that: (1) medium eccentricity shows a wider stable speed range; (2) rotor damping has little effect to the stability of the system; (3) lower mass ratio produces a stable response; (4) medium suspension/journal stiffness ratio contributes to a wider stable speed range; (5) a higher viscosity shows a wider stable speed range than lower viscosity. From the above results, the rotor bearing system shows complex nonlinear dynamic behavior with nonlinear viscous damping. These results will be helpful to carrying out the optimal design of the rotor bearing system.

Harmonic Oscillations of Nonlinear Two-Degree-of-Freedom Systems

1955 ◽  
Vol 22 (1) ◽  
pp. 107-110
Author(s):  
T. C. Huang
Keyword(s):  
Nonlinear System ◽  
Degrees Of Freedom ◽  
Forced Oscillations ◽  
Viscous Damping ◽  
Free Oscillations ◽  
Response Curves ◽  
Harmonic Oscillations ◽  
Restoring Force ◽  
Nonlinear Restoring Force ◽  
Two Degree Of Freedom

Abstract In this paper an investigation is made of equations governing the oscillations of a nonlinear system in two degrees of freedom. Analyses of harmonic oscillations are illustrated for the cases of (1) the forced oscillations with nonlinear restoring force, damping neglected; (2) the free oscillations with nonlinear restoring force, damping neglected; and (3) the forced oscillations with nonlinear restoring force, small viscous damping considered. Amplitudes of oscillations and frequency equations are derived based on the mathematically justified perturbation method. Response curves are then plotted.

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