Period-Doubling Bifurcation and Chaotic Phenomena in a Single Degree of Freedom Elastic System With A Two-State Variable Friction Law

2013 ◽  
pp. 75-80 ◽  
Author(s):  
Niu Zhiren ◽  
Chen Dangmin
Keyword(s):  
Elastic System ◽  
Period Doubling ◽  
Degree Of Freedom ◽  
Period Doubling Bifurcation ◽  
Single Degree Of Freedom ◽  
Friction Law ◽  
State Variable ◽  
Single Degree ◽  
Chaotic Phenomena ◽  
Variable Friction

Two Groups of Chaotic Vibrations in a Single-Degree-of-Freedom Maglev System

1997 ◽  
Author(s):  
Zhixiang Xu ◽  
Hideyuki Tamura
Keyword(s):  
Magnetic Levitation ◽  
Excitation Frequency ◽  
Power Spectra ◽  
Period Doubling ◽  
Excitation Amplitude ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Moving Base ◽  
Period Doubling Bifurcations

Abstract In this paper, a single-degree-of-freedom magnetic levitation dynamic system, whose spring is composed of a magnetic repulsive force, is numerically analyzed. The numerical results indicate that a body levitated by magnetic force shows many kinds of vibrations upon adjusting the system parameters (viz., damping, excitation amplitude and excitation frequency) when the system is excited by the harmonically moving base. For a suitable combination of parameters, an aperiodic vibration occurs after a sequence of period-doubling bifurcations. Typical aperiodic vibrations that occurred after period-doubling bifurcations from several initial states are identified as chaotic vibration and classified into two groups by examining their power spectra, Poincare maps, fractal dimension analyses, etc.

Effect of Third Harmonic Vibratory Force on a Linear Spring-Mass System

1963 ◽  
Vol 67 (636) ◽  
pp. 799-803
Author(s):  
C. L. Kirk
Keyword(s):  
Resonant Frequency ◽  
Elastic System ◽  
Rate Of Change ◽  
Degree Of Freedom ◽  
The Other ◽  
Mass System ◽  
Single Degree Of Freedom ◽  
Third Harmonic ◽  
Single Degree ◽  
Linear Spring

SummaryThe response of an elastic system having a single degree of freedom, to a vibratory force whose waveform can be varied, is examined. The variable waveform is produced by a system of two pairs of unbalanced rotors in which one pair rotates at three times the speed of the other pair. The waveform depends on the frequency of excitation, the phasing of the rotors and the ratio of their amounts of unbalance. If the rotors are run at a speed at which the faster pair rotates above resonance while the slower pair rotates below resonance, a frequency is found at which the rate of change of amplitude with respect to frequency is zero. At this point, however, the waveform is quite sensitive to small changes in the frequency of excitation. If the rotor speeds cannot be maintained constant, and if stable vibration waveforms are required, it is necessary to run the slowest rotor well above the resonant frequency where both the amplitude and waveform will be virtually independent of frequency.

scholarly journals Vibrations of fractional half- and single-degree of freedom systems

2017 ◽  
Vol 39 (3) ◽  
pp. 259-273
Author(s):  
Valentina Ciaschetti ◽  
Isaac Elishakoff ◽  
Alessandro Marzani
Keyword(s):  
Fractional Derivatives ◽  
Degree Of Freedom ◽  
Benchmark Problems ◽  
Matrix Approach ◽  
Single Degree Of Freedom ◽  
State Variable ◽  
Single Degree ◽  
Rational Order ◽  
Derivatives Of ◽  
Variable Analysis

In this paper we study vibrations of fractional oscillators by two methods: the triangular strip matrix approach, based on the Grunwald-Letnikov discretization of the fractional term, and the state variable analysis, which is suitable for systems with fractional derivatives of rational order. Some examples are solved in order to compare the two approaches and to conduct comparison with benchmark problems.

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