Effective Computation of the Poincaré Map for the Analysis of Nonlinear Dynamic Circuits/Systems Using Runge-Kutta Triples

Finger, Lutz; Uhlmann, Friedrich

doi:10.1142/s0218126694000065

Cited by 4 publications

(1 citation statement)

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“…For a periodic motion, there are a few of isolated points in the Poincaré map, For a chaotic behavior, the return points on the Poincaré map will form the geometrical fractal structure. 25–27 In conclusion, the behavior of the oil thickness of slipper/swash plate pair is in the periodic and steady motion.…”

Section: The Nonlinear Dynamic Analysis Of Csrmmentioning

confidence: 82%

Nonlinear dynamic modeling and analysis for aviation axial piston pump in center spring return mechanism

Hang¹,

Li²,

Zhang³

et al. 2019

Journal of Low Frequency Noise, Vibration and Active Control

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Aviation axial piston pump is an important energy conversion component in aircraft hydraulic system, and the study on the nonlinearity of key operating mechanism is very necessary for improving the reliable operation of the pump. Addressing the aviation axial piston pump, this article analyzes nonlinear dynamic characteristics of the center spring return mechanism by using theoretical analysis and numerical simulation. Firstly, mathematical models of oil-film forces of slipper/swash plate pair and cylinder/port plate pair are derived. Then, based on the nonlinear dynamic theory, some specific theoretical analysis methods such as Lyapunov index spectrum, bifurcation diagram, time series, phase plane portrait, Poincaré map, and power spectrum are used to carry out the numerical simulation of nonlinear dynamic behaviors. The result indicates that characteristics of the center spring can reveal the reason for the nonlinear vibration of the center spring return mechanism. Meanwhile, the behavior of the oil thickness of slipper/swash plate pair is in the periodic and steady motion, and the variation of the oil thickness of cylinder/port plate pair is in chaotic vibration, which establishes the theoretical foundation of the aviation axial piston pump for the traceability and suppression of vibration. The obtained results are of important guidance significance for optimal design and dynamic control of the center spring return mechanism of aviation axial piston pump.

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Section: The Nonlinear Dynamic Analysis Of Csrmmentioning

confidence: 82%

Nonlinear dynamic modeling and analysis for aviation axial piston pump in center spring return mechanism

Hang¹,

Li²,

Zhang³

et al. 2019

Journal of Low Frequency Noise, Vibration and Active Control

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The Josephson junction circuit family: network theory

Finger

2000

Int. J. Circ. Theor. Appl.

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Analysis of non‐linear dynamical circuits and systems under the influence of thermal noise

Finger

Uhlmann

1995

Circuit Theory & Apps

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SUMMARYIn some electronic systems, such as cryoelectronic circuits, random noise has to be taken into consideration for modelling and simulation. After theoretical considerations an algorithm for the simulation of non-linear circuits with random noise is developed. Methods for global analysis of non-linear dynamical systems, such as Lyapunov exponents and the Poincad map, are applied to systems with noise. The developed algorithms are applied to the cryoelectronic circuit of the ideal DC-SQUID model. Several non-linear effects which occur through noise are explained.

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Effective Computation of the Poincaré Map for the Analysis of Nonlinear Dynamic Circuits/Systems Using Runge-Kutta Triples

Cited by 4 publications

References 0 publications

Nonlinear dynamic modeling and analysis for aviation axial piston pump in center spring return mechanism

Nonlinear dynamic modeling and analysis for aviation axial piston pump in center spring return mechanism

The Josephson junction circuit family: network theory

Analysis of non‐linear dynamical circuits and systems under the influence of thermal noise

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