Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (5): 586-592.

• Articles • Previous Articles     Next Articles

A 1/3 PURE SUBHARMONIC SOLUTION AND TRANSIENT PROCESS FOR THE DUFFING’S EQUATION

XU Yu-xiu1,2, BAO Wen-bo3, W.Schiehlen3, HU Hai-yan4   

  1. 1. Department of Civil Engineering Shenyang University of Technology, Shenyang 110023, P. R. China;
    2. Northeast University, Shenyang, 110006, P. R. China;
    3. Institute B for machanic, University Stuttgart, Germany;
    4. Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China
  • Received:1999-10-18 Revised:2001-01-16 Online:2001-05-18 Published:2001-05-18
  • Supported by:

    the National Natural Science Foundation of China(59572024)

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.

2010 MSC Number: 

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