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A 1/3 Pure Subharmonic Solution and Transient Process for the Duffing's Equation

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Abstract

The 1/3 subharmonic solution for the Duffing's equation is investigated by using the methods of harmonic balance and numerical integration. The sensitivity of parameter variation for the transient process and the transient process for the perturbance initial conditions are studied. Over and above, the precision of numerical integration method is discussed and the numerical integration method is compared with the harmonic balance method. Finally, asymptotical stability of the pure subharmonic oscillations element is inspected.

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Authors and Affiliations

  1. Department of Civil Engineering, Shenyang University of Technology, Shenyang, 110023, P R China

    Yu-xiu Xu

  2. Northeast University, Shenyang, 110006, P R China

    Yu-xiu Xu

  3. Institute B for machanic, University Stuttgart, Germany

    Wen-bo Bao & W. Schiehlen

  4. Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, P R China

    Hai-yan Hu

Authors
  1. Yu-xiu Xu
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  2. Wen-bo Bao
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  3. W. Schiehlen
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  4. Hai-yan Hu
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Xu, Yx., Bao, Wb., Schiehlen, W. et al. A 1/3 Pure Subharmonic Solution and Transient Process for the Duffing's Equation. Applied Mathematics and Mechanics 22, 586–592 (2001). https://doi.org/10.1023/A:1016336121503

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  • DOI: https://doi.org/10.1023/A:1016336121503

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