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Title: Stochastic bifurcation and fractal and chaos control of a giant magnetostrictive film-shape memory alloy composite cantilever plate subjected to in-plane harmonic and stochastic excitation

Stochastic bifurcation and fractal and chaos control of a giant magnetostrictive film–shape memory alloy (GMF–SMA) composite cantilever plate subjected to in-plane harmonic and stochastic excitation were studied. Van der Pol items were improved to interpret the hysteretic phenomena of both GMF and SMA, and the nonlinear dynamic model of a GMF–SMA composite cantilever plate subjected to in-plane harmonic and stochastic excitation was developed. The probability density function of the dynamic response of the system was obtained, and the conditions of stochastic Hopf bifurcation were analyzed. The conditions of noise-induced chaotic response were obtained in the stochastic Melnikov integral method, and the fractal boundary of the safe basin of the system was provided. Finally, the chaos control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that stochastic Hopf bifurcation and chaos appear in the parameter variation process. The boundary of the safe basin of the system has fractal characteristics, and its area decreases when the noise intensifies. The system reliability was improved through stochastic optimal control, and the safe basin area of the system increased.
Authors:
 [1] ;  [2] ; ;  [1]
  1. Department of Mechanics, Tianjin University, Tianjin 300072 (China)
  2. (China)
Publication Date:
OSTI Identifier:
22273715
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Applied Physics; Journal Volume: 115; Journal Issue: 17; Conference: 55. annual conference on magnetism and magnetic materials, Atlanta, GA (United States), 14-18 Nov 2010; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ALLOYS; CHAOS THEORY; COMPUTERIZED SIMULATION; EXCITATION; FRACTALS; MAGNETOSTRICTION; NONLINEAR PROBLEMS; OPTIMAL CONTROL; PROBABILITY DENSITY FUNCTIONS; SHAPE MEMORY EFFECT; STOCHASTIC PROCESSES; THIN FILMS