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Mathematical Problems in Engineering
Volume 2014, Article ID 672547, 10 pages
http://dx.doi.org/10.1155/2014/672547
Research Article

Control of the Thermal Fractal Diffusion of Tightly Compressed Heterogeneous Layers of Thin Plates

1School of Control Science and Engineering, Shandong University, Jinan 250061, China
2School of Mechanical and Electrical Engineering, Shandong University at Weihai, Weihai 264209, China

Received 30 June 2014; Revised 28 September 2014; Accepted 30 September 2014; Published 5 November 2014

Academic Editor: Wang Xing-yuan

Copyright © 2014 Wei Qiao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

As the thermal conductivity of thin plates composed of tightly compressed heterogeneous layers varies continuously in the form of an exponential function, we present a nonlinear dynamical model of the fractal growth of thermal diffusion. We also analyze the quantitative relationship between the probability of growth and the disturbance term, predict the control action of the environmental disturbance term on fractal growth, and use Matlab simulation to verify the control effectiveness of thermal fractal diffusion. The results facilitate the selection of appropriate control areas and control parameters for the thermal diffusion variable coefficients. In addition, variation in the fractal dimension reflects the influence of environmental disturbance on the complex process of thermal fractal diffusion.