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 differentialequation 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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Contributed by Yupang Gui-tong, Original Member of Editorial Committee, AMM
Foundation items: the National Natural Science Foundation of China (10172063); Shanxi Foundation of Science and Technology (20001007); the Key Project of Ninth Five-Year Plan of National Natural Science Foundation of China (19990510)
Biography: Lupi Yin-shan (1961≈)
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Yin-shan, L., Nian-mei, Z. & Gui-tong, Y. 1/3 subharmonic solution of elliptical sandwich plates. Appl Math Mech 24, 1147–1157 (2003). https://doi.org/10.1007/BF02438104
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DOI: https://doi.org/10.1007/BF02438104
Key words
- elliptical sandwich plate
- superpositive-iterative harmonic balance (SIHB) method
- 1/3 subharmonic solution
- bifurcation