1/3 SUBHARMONIC SOLUTION OF ELLIPTICAL SANDWICH PLATES  

作　　者：李银山 张年梅 杨桂通 

机构地区：[1]Institute of Engineering Mechanics, Hebei University of Technology [2]Institute of Applied Mechanics, Taiyuan University of Technology, Taiyuan 030024, P.R.China [3]Institute of Applied Mechanics, Taiyuan University of Technology

出　　处：《Applied Mathematics and Mechanics(English Edition)》2003年第10期1147-1157,共11页应用数学和力学（英文版）

基　　金：theNationalNaturalScienceFoundationofChina (1 0 1 72 0 63 ) ;ShanxiFoundationofScienceandTechnology (2 0 0 0 1 0 0 7) ;theKeyProjectofNinthFive_YearPlanofNationalNaturalScienceFoundationofChina (1 9990 51 0 )

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.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.

关 键 词：elliptical sandwich plate superpositive-iterative harmonic balance  (SIHB) method 1/3 subharmonic solution BIFURCATION 

分 类 号：O322[理学—一般力学与力学基础] O343.9[理学—力学]