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Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (10): 1147-1157.

• 论文 • 上一篇    下一篇

1/3 SUBHARMONIC SOLUTION OF ELLIPTICAL SANDWICH PLATES

李银山1,2, 张年梅2, 杨桂通2   

  1. 1. Institute of Engineering Mechanics, Hebei University of Technology, Tianjin 300130, P. R. China;
    2. Institute of Applied Mechanics, Taiyuan University of Technology, Taiyuan 030024, P. R. China
  • 收稿日期:2002-01-29 修回日期:2003-05-27 出版日期:2003-10-18 发布日期:2003-10-18
  • 基金资助:
    the National Natural Science Foundation of China (10172063); Shanxi Foundation of Science and Technology(20001007); the Key Project of Ninth Five-Year Plan of NationalNatural Science Foundation of China (19990510)

1/3 SUBHARMONIC SOLUTION OF ELLIPTICAL SANDWICH PLATES

LI Yin-shan1,2, ZHANG Nian-mei2, YANG Gui-tong2   

  1. 1. Institute of Engineering Mechanics, Hebei University of Technology, Tianjin 300130, P. R. China;
    2. Institute of Applied Mechanics, Taiyuan University of Technology, Taiyuan 030024, P. R. China
  • Received:2002-01-29 Revised:2003-05-27 Online:2003-10-18 Published:2003-10-18
  • Supported by:
    the National Natural Science Foundation of China (10172063); Shanxi Foundation of Science and Technology(20001007); the Key Project of Ninth Five-Year Plan of NationalNatural Science Foundation of China (19990510)

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摘要： The problem of nonlinear forced oscillations for elliptical sandwich plates is dealt with. Based on the governing equations expressed in terms of five displacement components, the nonlinear dynamic equation of an elliptical sandwich plate under a harmonic force is derived. A superpositive-iterative harmonic balance (SIHB) method is presented for the steady-state analysis of strongly nonlinear oscillators. In a periodic oscillation, the periodic solutions can be expressed in the form of basic harmonics and bifurcate harmonics. Thus, an oscillation system which is described as a second order ordinary differential equation, can be expressed as fundamental differential equation with fundamental harmonics and incremental differential equation with derived harmonics. The 1/3 subharmonic solution of an elliptical sandwich plate is investigated by using the methods of SIHB. The SIHB method is compared with the numerical integration method. Finally, asymptotical stability of the 1/3 subharmonic oscillations is inspected.

Abstract: The problem of nonlinear forced oscillations for elliptical sandwich plates is dealt with. Based on the governing equations expressed in terms of five displacement components, the nonlinear dynamic equation of an elliptical sandwich plate under a harmonic force is derived. A superpositive-iterative harmonic balance (SIHB) method is presented for the steady-state analysis of strongly nonlinear oscillators. In a periodic oscillation, the periodic solutions can be expressed in the form of basic harmonics and bifurcate harmonics. Thus, an oscillation system which is described as a second order ordinary differential equation, can be expressed as fundamental differential equation with fundamental harmonics and incremental differential equation with derived harmonics. The 1/3 subharmonic solution of an elliptical sandwich plate is investigated by using the methods of SIHB. The SIHB method is compared with the numerical integration method. Finally, asymptotical stability of the 1/3 subharmonic oscillations is inspected.

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