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Dynamic behaviors of nonlinear fractional-order differential oscillator

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Abstract

The nonlinear dynamic behaviors of oscillators described by fractional-order differential are presented in this paper. The background of the research is based upon two engineering practices. First is that the visco-elastic behaviors of some advanced polymeric materials can be accurately modeled by the fractional calculus constitutive law. Second is that the influence of nonlinear visco-elasticity described by the fractional operator cannot be neglected in some cases such as the vibration with large displacement or large strain and thermo-visco-elastic coupled problems. The numerical scheme for solving the nonlinear equation of motion is developed. The results show that because of the introduction of nonlinear damping modeled by the fractional-order operator, the bifurcation and chaos of the oscillator appear in forced vibration. Furthermore, the fraction value of the fractional operator evidently affects the dynamic behavior of the nonlinear fractional differential oscillator.

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Authors and Affiliations

  1. Department of Electronic Engineering, JiNan University, Guangzhou, China

    Wei Zhang

  2. Institute of Mechanical Science and Technology, Shenzhen, China

    Shao-kai Liao

  3. Department of Mechanical and Power Engineering, Iwaki Meisei University, Iwaki, Japan

    Nobuyuki Shimizu

Authors
  1. Wei Zhang
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  2. Shao-kai Liao
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  3. Nobuyuki Shimizu
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Corresponding author

Correspondence to Wei Zhang.

Additional information

Wei Zhang received his doctorate degree in Mechanics at Xi’an Jiaotong University in China in 1994. He went to the University Of Sheffield in the UK as an academic visitor from July 1986 to July 1987. He completed his post-doctorate study in Iwaki Meisei University in Japan through the support of the JSPS from May 1997 to June 1999. Dr. Zhang is currently a professor at the Department of Electronic Engineering of JiNan University in Guangzhou, China.

Shao-kai Liao received his B.E. degree in Civil Engineering at JiNan University in Guangzhou, China in 2004 and his master’s degree in Engineering Mechanics at the same university in 2006. Mr. Liao was once a postgraduate student of Professor Wei Zhang, and he now works in an institute in Shenzhen City in China.

Nobuyuki Shimizu received his B.S. degree in Mechanical Engineering at Yokohama National University and his master’s and doctorate degrees in Mechanical Engineering at University of Tokyo in 1968 and 1971, respectively. He went to the California Institute of Technology in California, U.S.A. as a visiting associate from October 1976 to September 1977. Dr. Shimizu is currently a professor at the Department of Mechanical and Power Engineering of Iwaki Meisei University in Japan.

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Zhang, W., Liao, Sk. & Shimizu, N. Dynamic behaviors of nonlinear fractional-order differential oscillator. J Mech Sci Technol 23, 1058–1064 (2009). https://doi.org/10.1007/s12206-009-0341-4

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  • DOI: https://doi.org/10.1007/s12206-009-0341-4

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