Hysteretic dynamics inducing coexistence of attractors in a thin magnetostrictive actuator system with quintic nonlinearity

Abstract This paper introduces and investigates the dynamics of a thin magnetostrictive actuator with quintic nonlinearity. The energy balance method is used to carry out the motion equation of the system. The analytical solutions and amplitude responses of the system are exanimated using the multiple time scale method. The dynamical behavior of the system is explored with the help of common nonlinear tools such as bifurcation diagrams with Lyapunov exponents, time series plots, phase portraits and basin of attraction. The bifurcation diagrams reveal that the system under study exhibits complicated dynamics including crisis route to chaos, multistability and antimonotonicity. To validate the theoretical and numerical analyses, an electronic circuit capable to describe the dynamics of the system is designed and implemented in PSpice software. A very good agreement is observed between PSpice based circuit simulations and theoretical/numerical results.

[1]  Xiaojing Zheng,et al.  A one-dimension coupled hysteresis model for giant magnetostrictive materials , 2007 .

[2]  Jacques Kengne,et al.  Coexistence of Multiple Attractors and Crisis Route to Chaos in a Novel Chaotic Jerk Circuit , 2016, Int. J. Bifurc. Chaos.

[3]  Toshiro Higuchi,et al.  “Zero-power” positioning actuator for cryogenic environments by combining magnetostrictive bimetal and HTS , 2007 .

[4]  Alison B. Flatau,et al.  An Energy-Based Hysteresis Model for Magnetostrictive Transducers , 1997 .

[5]  Abdul-Ghani Olabi,et al.  Design of a magnetostrictive (MS) actuator , 2008 .

[6]  C. Hong.  Rapid Heating Induced Vibration of Magnetostrictive Functionally Graded Material Plates , 2012 .

[7]  Ulrich Parlitz,et al.  Superstructure in the bifurcation set of the Duffing equation ẍ + dẋ + x + x3 = f cos(ωt) , 1985 .

[8]  Shandelle M Henson,et al.  Multiple mixed-type attractors in a competition model , 2007, Journal of biological dynamics.

[9]  J. Yorke,et al.  Antimonotonicity: inevitable reversals of period-doubling cascades , 1992 .

[10]  Youhe Zhou,et al.  A nonlinear transient constitutive model with eddy current effects for giant magnetostrictive materials , 2010 .

[11]  Leon O. Chua,et al.  EXPERIMENTAL OBSERVATION OF ANTIMONOTONICITY IN CHUA'S CIRCUIT , 1993 .

[12]  Z. Cao,et al.  Design of a giant magnetostrictive motor driven by elliptical motion , 2005 .

[13]  C. Hong,et al.  Application of a magnetostrictive actuator , 2013 .

[14]  Wenmei Huang,et al.  Hybrid genetic algorithms for parameter identification of a hysteresis model of magnetostrictive actuators , 2007, Neurocomputing.

[15]  K. Kyamakya,et al.  On the analysis of semiconductor diode-based chaotic and hyperchaotic generators—a case study , 2014 .

[16]  P. Krishnaprasad,et al.  On a low-dimensional model for ferromagnetism , 2005 .

[17]  R. D. Greenough,et al.  Actuation and transduction by giant magnetostrictive alloys , 2000 .

[18]  Krzysztof Chwastek,et al.  An alternative method to estimate the parameters of Jiles–Atherton model , 2007 .

[19]  Stephen Lynch,et al.  Dynamical Systems with Applications using Mathematica , 2007 .

[20]  L. Qin,et al.  Vibration Analysis of Linear Magnetostrictive Actuator , 2011 .

[21]  A. Olabi,et al.  Design and application of magnetostrictive materials , 2008 .

[22]  Masoller.  Coexistence of attractors in a laser diode with optical feedback from a large external cavity. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[23]  Ioannis M. Kyprianidis,et al.  A chaotic path planning generator for autonomous mobile robots , 2012, Robotics Auton. Syst..

[24]  E. Foadieng,et al.  Research Article A Model for a Thin Magnetostrictive Actuator in Nonlinear Dynamics , 2015 .

[25]  Ioannis M. Kyprianidis,et al.  Image encryption process based on chaotic synchronization phenomena , 2013, Signal Process..

[26]  Jacques Kengne,et al.  Dynamical analysis of a novel autonomous 4-D hyperjerk circuit with hyperbolic sine nonlinearity: Chaos, antimonotonicity and a plethora of coexisting attractors , 2018 .

[27]  Ioannis M. Kyprianidis,et al.  Experimental investigation on coverage performance of a chaotic autonomous mobile robot , 2013, Robotics Auton. Syst..