Mathematical model for dynamic hysteresis loops

1971 ◽  
Vol 9 (5) ◽  
pp. 435-450 ◽  
Author(s):  
Leon O. Chua ◽  
Keith A. Stromsmoe
Keyword(s):  
Mathematical Model ◽  
Hysteresis Loops ◽  
Dynamic Hysteresis

A SIMPLE DYNAMIC PREISACH HYSTERESIS MODEL FOR FeSi MATERIALS

2003 ◽  
Vol 17 (11) ◽  
pp. 2325-2331
Author(s):  
M. LU ◽  
P. J. LEONARD ◽  
P. MARKETOS ◽  
T. MEYDAN ◽  
A. J. MOSES
Keyword(s):  
Applied Field ◽  
Hysteresis Loops ◽  
Cosine Function ◽  
Preisach Model ◽  
Common Phenomenon ◽  
Hysteresis Model ◽  
Dynamic Hysteresis ◽  
Model Based ◽  
Hysteresis Operator ◽  
Preisach Hysteresis

Dynamic hysteresis property is a common phenomenon in FeSi materials under time-varied applied field. This paper presented a dynamic hysteresis model based on Preisach scheme. The rectangular-shaped elementary hysteresis operator with two states in classical Preisach model is replaced by a non-rectangular shaped one with multiple states. The output of each state is calculated by a cosine function. The proposed dynamic hysteresis model is experimently tested by comparing the simulated hysteresis loops to experimental ones. The model can be used to describe the dynamic hysteresis in FeSi material for magnetizing frequencies from quasi-static to several hundred Hertz.

scholarly journals Research of Jiles-Atherton Dynamic Model in Giant Magnetostrictive Actuator

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Yongguang Liu ◽  
Xiaohui Gao ◽  
Chunxu Chen
Keyword(s):  
Mathematical Model ◽  
Dynamic Model ◽  
Control Strategies ◽  
Structural Parameters ◽  
Hysteresis Loops ◽  
Structural Dynamic ◽  
Magnetostrictive Actuator ◽  
Output Characteristics ◽  
And Control ◽  
Minor Hysteresis Loops

Due to the existence of multicoupled nonlinear factors in the giant magnetostrictive actuator (GMA), building precise mathematical model is highly important to study GMA’s characteristics and control strategies. Minor hysteresis loops near the bias magnetic field would be often applied because of its relatively good linearity. Load, friction, and disc spring stiffness seriously affect the output characteristics of the GMA in high frequency. Therefore, the current-displacement dynamic minor loops mathematical model coupling of electric-magnetic-machine is established according to Jiles-Atherton (J-A) dynamic model of hysteresis material, GMA structural dynamic equation, Ampere loop circuit law, and nonlinear piezomagnetic equation and demonstrates its correctness and effectiveness in the experiments. Finally, some laws are achieved between key structural parameters and output characteristics of GMA, which provides important theoretical foundation for structural design.

scholarly journals The theorem about the transformer excitation current waveform mapping into the dynamic hysteresis loop branch for the sinusoidal magnetic flux case

2015 ◽  
Vol 12 (1) ◽  
pp. 33-52
Author(s):  
Nenad Petrovic ◽  
Velibor Pjevalica ◽  
Vladimir Vujicic
Keyword(s):  
Magnetic Flux ◽  
Hysteresis Loop ◽  
Hysteresis Loops ◽  
Stationary Regime ◽  
Interpolation Polynomial ◽  
Magnetic Core ◽  
Excitation Current ◽  
Approximation Accuracy ◽  
Dynamic Hysteresis ◽  
Chebyshev Nodes

This paper analyses aspects of the approximation theory application on the certain subsets of the measured samples of the transformer excitation current and the sinusoidal magnetic flux. The presented analysis is performed for single-phase transformer case, Epstein frame case and toroidal core case. In the paper the theorem of direct mapping the transformer excitation current in the stationary regime is proposed. The excitation current is mapped to the dynamic hysteresis loop branch (in further text DHLB) by an appropriate cosine transformation. This theorem provides the necessary and satisfactory conditions for above described mapping. The theorem highlights that the transformer excitation current under the sinusoidal magnetic flux has qualitatively equivalent information about magnetic core properties as the DHLB. Furthermore, the theorem establishes direct relationship between the number of the transformer excitation current harmonics and their coefficients with the degree of the DHLB interpolation polynomial and its coefficients. The DHLB interpolation polynomial is calculated over the measured subsets of samples representing Chebyshev nodes of the first and the second kind. These nonequidistant Chebyshev nodes provides uniform convergence of the interpolation polynomial to the experimentally obtained DHLB with an excellent approximation accuracy and are applicable on the approximation of the static hysteresis loops and the DC magnetization curves as well.

Modeling vibrations of a beam with one fixed and another free end using fractional integrodifferentiation

2020 ◽  
Vol 20 (3) ◽  
pp. 19-23
Author(s):  
S.Sh. Rekhviashvili ◽  
◽  
A.V. Pskhu ◽  
A.M. Kidakoev ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Model Equation ◽  
Analytical Form ◽  
Dynamic Hysteresis ◽  
Fractional Integrodifferentiation

A mathematical model of vibrations of a beam with one fixed and another free end has been developed, taking into account the effect of dynamic hysteresis, which is described using fractional integro-differentiation. The solution of the model equation is found in analytical form. The use of the fractional integro-differentiation makes it possible to correctly describe the dissipative nature of the beam vibrations.

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