Experimental Study of a Symmetrical Piecewise Base-Excited Oscillator

1998 ◽  
Vol 65 (3) ◽  
pp. 657-663 ◽  
Author(s):  
M. Wiercigroch ◽  
V. W. T. Sin
Keyword(s):  
Experimental Study ◽  
Periodic Motion ◽  
Chaotic Motion ◽  
Piecewise Linear ◽  
Calibration Procedure ◽  
Experimental Setup ◽  
Stiffness Ratio ◽  
Bifurcation Diagrams ◽  
Parameter Values ◽  
Excited Oscillator

This paper presents an experimental study on a base-excited piecewise linear oscillator with symmetrical flexible constrains of high stiffness ratio (above 20). The details of the adopted design of the oscillator, the experimental setup, and calibration procedure are briefly discussed. The regions of chaotic motion predicted theoretically were confirmed by the experimental results arranged into bifurcation diagrams. Clearance, stiffness ratio, amplitude, and frequency of the external force were used as branching parameters. The discussion of the system dynamics is based on bifurcation diagrams and Lissajous curves. The investigated system tends to be periodic for large clearances and chaotic for small ones. This picture is reversed for the amplitude of the forcing changes, where periodic motion occurred for small values and chaos dominated for larger forcing. The same behavior is observed for increasing frequency ratio where, for values below the natural frequency, the most interesting dynamics occurs. For the investigated parameter values, the stiffness ratio variation produces only periodic motion.

AN OSCILLATOR WITH CUBIC AND PIECEWISE-LINEAR SPRINGS

1991 ◽  
Vol 01 (02) ◽  
pp. 349-356 ◽  
Author(s):  
YOHANNES KETEMA
Keyword(s):  
Parameter Space ◽  
Periodic Motion ◽  
Chaotic Motion ◽  
Piecewise Linear ◽  
Cubic Nonlinearity ◽  
Nonlinear Spring ◽  
Resonant Orbits ◽  
Offset Distance ◽  
Linear Spring ◽  
Parameter Values

A system consisting of a mass attached to a nonlinear spring with negative linear stiffness and cubic nonlinearity, (i.e., a spring obeying Duffing's equation with negative linear stiffness) and a linear spring at a certain offset distance is studied. Melnikov's method is applied to determine the existence of homoclinic points for the Poincare map, and preserved resonant orbits and boundaries for these are given in the parameter space. This system is then compared to the system consisting of only the nonlinear spring with regard to the existence of parameter regimes where chaotic motion is possible. It is shown that if the linear spring is of appropriate stiffness the chaotic motion for a given set of parameter values occurring for the system consisting of only the nonlinear spring is replaced by periodic motion and the mechanism of this phenomenon is explained.

Dynamics analysis of a gyrostat system with intermittent forcing

2021 ◽  
pp. 095965182110590
Author(s):  
Jianbin He ◽  
Jianping Cai
Keyword(s):  
Lyapunov Exponent ◽  
Numerical Simulations ◽  
Periodic Motion ◽  
Chaotic Motion ◽  
Dynamics Analysis ◽  
Bifurcation Diagrams ◽  
Stable Point ◽  
Dynamical Characteristics ◽  
Main Work ◽  
Selection Of

The dynamical characteristics of a gyrostat system with intermittent forcing are investigated, the main work and contributions are given as follows: (1) The gyrostat system with an intermittent forcing is studied, and its dynamical characteristics are investigated by the corresponding Lyapunov exponent spectrums and bifurcation diagrams with respect to the amplitude of intermittent forcing. The modified gyrostat system exists chaotic motion when the amplitude of intermittent forcing belongs to a certain interval, and it can be at a state of stable point or periodic motion by the design of amplitude. (2) The gyrostat system with multiple intermittent forcings is also investigated through the combination of Lyapunov exponent spectrums and bifurcation diagrams, and it behaves periodic motion or chaotic motion when the amplitude or forcing width is different. (3) By the selection of parameters in intermittent forcings, the modified gyrostat system is at a state of stable point, periodic motion or chaotic motion. Numerical simulations verify the feasibility and effectiveness of the modified gyrostat system.

Detecting Parameter Changes Using Experimental Nonlinear Dynamics and Chaos

1996 ◽  
Vol 118 (3) ◽  
pp. 375-383 ◽  
Author(s):  
R. S. Chancellor ◽  
R. M. Alexander ◽  
S. T. Noah
Keyword(s):  
Nonlinear Dynamics ◽  
Periodic Orbits ◽  
Piecewise Linear ◽  
Phase Portraits ◽  
Unstable Periodic Orbits ◽  
Bifurcation Diagrams ◽  
Frequency Spectra ◽  
Nonlinear Dynamics And Chaos ◽  
Chaotic Nature ◽  
Parameter Values

A method of detecting parameter changes using analytical and experimental nonlinear dynamics and chaos is applied to a piecewise-linear oscillator. Experimental data show the chaotic nature of the system through phase portraits, Poincare´ maps, frequency spectra and bifurcation diagrams. Unstable periodic orbits were extracted from each chaotic time series obtained from the system with six different parameter values. Movement of the unstable periodic orbits in phase space is used to detect parameter changes in the system.

scholarly journals Differential Transform Method as an Effective Tool for Investigating Fractional Dynamical Systems

2021 ◽  
Vol 11 (15) ◽  
pp. 6955
Author(s):  
Andrzej Rysak ◽  
Magdalena Gregorczyk
Keyword(s):  
Optimal Parameter ◽  
Differential Transform Method ◽  
Bifurcation Diagrams ◽  
Transform Method ◽  
Rossler System ◽  
Differential Transform ◽  
Rössler System ◽  
Fractional System ◽  
Parameter Values

This study investigates the use of the differential transform method (DTM) for integrating the Rössler system of the fractional order. Preliminary studies of the integer-order Rössler system, with reference to other well-established integration methods, made it possible to assess the quality of the method and to determine optimal parameter values that should be used when integrating a system with different dynamic characteristics. Bifurcation diagrams obtained for the Rössler fractional system show that, compared to the RK4 scheme-based integration, the DTM results are more resistant to changes in the fractionality of the system.

EXPERIMENTAL STUDY OF CFOA-BASED INDUCTORLESS CHUA'S CIRCUIT

2004 ◽  
Vol 14 (04) ◽  
pp. 1369-1374 ◽  
Author(s):  
RECAI KILIÇ
Keyword(s):  
Experimental Study ◽  
High Frequency ◽  
Chaotic Behavior ◽  
Comparative Investigation ◽  
Experimental Setup ◽  
Chua’S Circuit ◽  
Current Feedback ◽  
Chua's Circuit ◽  
Op Amps ◽  
High Frequency Performance

The current feedback op amps (CFOAs), with some significant advantages over the conventional op amps, have been used instead of voltage op amps (VOAs) in new implementations of Chua's circuit. In our previous study, after providing a comparative investigation of CFOA-based realizations of Chua's circuit in the literature, we have also presented an alternative inductorless CFOA-based realization of Chua's circuit, and the circuit's chaotic behavior by Pspice simulations. In this paper, we investigate CFOA-based Chua's circuit by constructing an experimental setup, and testing the performance of the proposed implementation at different frequencies. Its excellent high frequency performance was experimentally verified.

scholarly journals An experimental study of the dynamics of ascent of the bubble system in the presence of a surfactant

2018 ◽  
Vol 194 ◽  
pp. 01002
Author(s):  
Alexandra Antonnikova ◽  
Sergey Basalaev ◽  
Anna Usanina ◽  
Eugene Maslov
Keyword(s):  
Experimental Study ◽  
Reynolds Numbers ◽  
Experimental Setup ◽  
Bubble Cluster ◽  
Bubble System ◽  
Wide Range ◽  
Compact Cluster ◽  
Glycerol Medium

This paper presents investigations on the new experimental setup for obtaining a compact cluster of monodisperse bubbles of a given diameter is presented. Also we provided the results of experimental study of the bubble cluster floating-up in the presence of a surfactant in a wide range of Reynolds numbers. There was held a comparison of the dynamics of the floating-up of a monodisperse bubble cluster in a glycerol medium and in the medium glycerin supplemented with a surfactant.

Experimental Study on Numerical Controlled Electrochemical Turning

2010 ◽  
Vol 426-427 ◽  
pp. 658-663 ◽  
Author(s):  
Min Kang ◽  
X.Q. Fu ◽  
Yong Yang
Keyword(s):  
Experimental Study ◽  
Surface Roughness ◽  
Flow Field ◽  
Rotational Speed ◽  
Cylindrical Surface ◽  
Special Kind ◽  
Machining Process ◽  
Experimental Setup ◽  
Electrolyte Flow ◽  
Electrochemical Turning

In order to machine revolving workpieces which are made of difficult-to-cut materials or have low rigidity, the technology of Numerical Controlled Electrochemical Turning (NC-ECT) was put forward and the preliminary experimental study was presented in this paper. To carry out the study, an experimental setup was developed, and a new special kind of inner-spraying cathode with single linear edge was designed according to the process of machining cylindrical surface and the requirement of stable electrolyte flow field. First, the NC-ECT method was simply described. Then, considering the structure of the cathode and the machining process, the method for calculating the material removed depth per revolution in machining the cylindrical surface was given. Finally, the experiments of machining the cylindrical surface were carried out. Experiments showed: 1) The calculated material removed depth per revolution is well consistent with the actual value of the machining process, which decreases with the increase of the rotational speed of the workpiece and increases almost linearly with the increase of the working voltage; 2) The surface roughness decreases with the increase of the rotational speed of the workpiece and the working voltage; 3) The working current in the machining process trend to stable after several revolutions.

Arbitrary Periodic Motions and Grazing Switching of a Forced Piecewise Linear, Impacting Oscillator

2006 ◽  
Vol 129 (3) ◽  
pp. 276-284 ◽  
Author(s):  
Albert C. J. Luo ◽  
Lidi Chen
Keyword(s):  
Nonlinear Dynamics ◽  
Periodic Motion ◽  
Local Stability ◽  
Piecewise Linear ◽  
Analytical Prediction ◽  
Periodic Motions ◽  
Grazing Bifurcation ◽  
Piecewise Linear System ◽  
Local Stability Analysis ◽  
Mapping Structures

The grazing bifurcation and periodic motion switching of the harmonically forced, piecewise linear system with impacting are investigated. The generic mappings relative to the discontinuous boundaries of this piecewise system are introduced. Based on such mappings, the corresponding grazing conditions are obtained. The mapping structures are developed for the analytical prediction of periodic motions in such a system. The local stability and bifurcation conditions for specified periodic motions are obtained. The regular and grazing, periodic motions are illustrated. The grazing is the origin of the periodic motion switching for this system. Such a grazing bifurcation cannot be estimated through the local stability analysis. This model is applicable to prediction of periodic motions in nonlinear dynamics of gear transmission systems.

Experimental Forced Response Analysis of Two-Degree-of-Freedom Piecewise-Linear Systems With a Gap

2020 ◽  
Author(s):  
Akira Saito ◽  
Junta Umemoto ◽  
Kohei Noguchi ◽  
Meng-Hsuan Tien ◽  
Kiran D’Souza
Keyword(s):  
Piecewise Linear ◽  
Excitation Frequency ◽  
Forced Response ◽  
Degree Of Freedom ◽  
Linear Oscillator ◽  
Phase Portraits ◽  
Response Analysis ◽  
Experimental Setup ◽  
The Masses ◽  
Two Degree Of Freedom

Abstract In this paper, an experimental forced response analysis for a two degree of freedom piecewise-linear oscillator is discussed. First, a mathematical model of the piecewise linear oscillator is presented. Second, the experimental setup developed for the forced response study is presented. The experimental setup is capable of investigating a two degree of freedom piecewise linear oscillator model. The piecewise linearity is achieved by attaching mechanical stops between two masses that move along common shafts. Forced response tests have been conducted, and the results are presented. Discussion of characteristics of the oscillators are provided based on frequency response, spectrogram, time histories, phase portraits, and Poincaré sections. Period doubling bifurcation has been observed when the excitation frequency changes from a frequency with multiple contacts between the masses to a frequency with single contact between the masses occurs.

scholarly journals Nonlinear Dynamic Analysis of Rotor Rub-Impact System

2019 ◽  
Vol 2019 ◽  
pp. 1-20
Author(s):  
Youfeng Zhu ◽  
Zibo Wang ◽  
Qiang Wang ◽  
Xinhua Liu ◽  
Hongyu Zang ◽  
...  
Keyword(s):  
Periodic Motion ◽  
Chaotic Motion ◽  
Nonlinear Dynamic Analysis ◽  
Period Doubling ◽  
Time History ◽  
Rotor System ◽  
Quasiperiodic Motion ◽  
Rotor Bearing ◽  
Motion Period ◽  
Bearing System

A dynamic model of a double-disk rub-impact rotor-bearing system with rubbing fault is established. The dynamic differential equation of the system is solved by combining the numerical integration method with MATLAB. And the influence of rotor speed, disc eccentricity, and stator stiffness on the response of the rotor-bearing system is analyzed. In the rotor system, the time history diagram, the axis locus diagram, the phase diagram, and the Poincaré section diagram in different rotational speeds are drawn. The characteristics of the periodic motion, quasiperiodic motion, and chaotic motion of the system in a given speed range are described in detail. The ways of the system entering and leaving chaos are revealed. The transformation and evolution process of the periodic motion, quasiperiodic motion, and chaotic motion are also analyzed. It shows that the rotor system enters chaos by the way of the period-doubling bifurcation. With the increase of the eccentricity, the quasi-periodicity evolution is chaotic. The quasiperiodic motion evolves into the periodic three motion phenomenon. And the increase of the stator stiffness will reduce the chaotic motion period.

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