Bifurcation and chaos characteristics of hysteresis vibration system of giant magnetostrictive actuator*

Abstract

Chaotic motion and quasi-periodic motion are two common forms of instability in the giant magnetostrictive actuator (GMA). Therefore, in the present study we intend to investigate the influences of the system damping coefficient, system stiffness coefficient, disc spring cubic stiffness factor, and the excitation force and frequency on the output stability and the hysteresis vibration of the GMA. In this regard, the nonlinear piezomagnetic equation, Jiles–Atherton hysteresis model, quadratic domain rotation model, and the GMA structural dynamics are used to establish the mathematical model of the hysteresis vibration system of the GMA. Moreover, the multi-scale method and the singularity theory are used to determine the co-dimensional two-bifurcation characteristics of the system. Then, the output response of the system is simulated to determine the variation range of each parameter when chaos is imposed. Finally, the fourth-order Runge–Kutta method is used to obtain the time domain waveform, phase portrait and Poincaré mapping diagrams of the system. Subsequently, the obtained three graphs are analyzed. The obtained results show that when the system output is stable, the variation range of each parameter can be determined. Moreover, the stability interval of system damping coefficient, system stiffness coefficient, and the coefficient of the cubic stiffness term of the disc spring are obtained. Furthermore, the stability interval of the exciting force and the excitation frequency are determined.

Simulation and optimization of bias magnetic field for giant magnetostrictive ultrasonic guided wave transducer

“…The experiment showed that the bias magnetic field provided by permanent magnet had a low displacement peak, but the difference was small and the heat dissipation was good.It can greatly improve the control accuracy and working time of GMEHA, and provide a reference for the selection of magnetic field bias mode in the subsequent research.Chen S et al 4 compared the open and closed state of the magnetic circuit and verified that the magnetic field in the GMM bar of the closed magnetic circuit has greater intensity, greater uniformity and smaller fluctuation range, and that the permanent magnet can provide a stable magnetic field to avoid the phenomenon of "frequency doubling".Liu Q et al 5 used the finite element software to optimize the magnetic circuit gap size of the giant magnetostrictive transducer. The results showed that the magnetic field strength and uniformity decreased with the increase of the gap, and the groove width of the optimal magnetic cylinder was determined through experiments.Yan H.B et al 6 compared the thickness, radius and other parameters of permanent magnets in the biased magnetic field with the magnetic field of the closed magnetic circuit, obtained the distribution uniformity of the axial magnetic field in the GMM rod, selected the best response parameter values, verified the corresponding relationship between the output displacement and the magnetic field uniformity, and further optimized the magnetic field uniformity.Gao X.H et al 7 used Ansoft Maxwell simulation software to design magnetic conductive end caps at both ends of magnetic circuits to suppress magnetic leakage. By changing the diameter and thickness of the end caps,the functional relationship between these two parameters and the maximum magnetic field intensity was compared and analyzed, and the end cap parameters at the maximum magnetic field intensity were obtained.Du G.X et al 8 built a test platform for the characteristics of giant magnetostrictive bars, which could measure the B-H curve and Young's modulus of GMM bars and other properties and parameters, providing feasible experimental support for the finite element simulation test.…”

Chaotic Characteristic Analysis of Spillway Radial Gate Vibration under Discharge Excitation

“…However, the method of the hydroelastic test that they adopted could be somewhat different from the actual operation of the gate. Yang et al [15] used the chaos theory to analyze the prototype test data of the supporting arm during the flood discharge. Both studies adopted the five-point cubic smoothing method to reduce the noise in the data, which can lead to the loss of critical vibration characteristics.…”

Explosive synchronization: From synthetic to real-world networks

“…[28] For example, complete, [27] phase, [29] time-scale, [30] lag, [31] and generalized [32] synchronization. The chaotic systems have been widely investigated and used in communication, [33] physics, [34] mechanics, [35] and biological [36] fields. In some chaotic systems, the basin of attraction has different regions that correspond to an attractor.…”