tailieunhanh - A note on the method of harmonic balance

Free oscillation period of the Duffing oscillator with cubic non-linearity was examined. A comparison between the exact period and those obtained by the asymptotic and the harmonic balance methods was done. It was shown that the reimlts given by the harmonic balance are acceptable even for large oscillations whereas the asymptotic method can only be applied for small oscillations. | Vietnam Journal of Mechanics, NCST of Vietnam Vol. 23, 2001 , No 1 (34 - 38) A NOTE ON THE METHOD OF HARMONIC BALANCE NGUYEN VAN DINH Institute of Mechanics, NCST of Vietnam was ABSTRACT. Free oscillation period of the Duffing oscillator with cubic non-linearity examined. A comparison between the exact period and those obtained by the asymptotic an Ao*). This work was supported by the Council for Natural Science of Vietnam. REFERENCES 1. Cheung Y. K., Chen S. H. and Lau S. L. A modified Lindstedt-Poincare method for certain ]strongly non-linear oscillators, Int. J . Non-Linear Mechanics, Vol. 26, No 3/4, 1991, pp. 367-378. 2. Nayfeh A. H. Introduction to perturbation techniques, Wiley, New York, 1981. 3. Mitropolski Yu. A., Nguyen Van Dao. Applied Asymptotic Methods in Nonlinear Oscillations. Khiwer Acadernjc Publishers, Dordrecht, Netherlands, 1997. Received November 29, 2000 GHI CHU VE PHUONG PHAP CAN BANG DIEU HOA Xet chu ky dao d(_)ng tv do cua chan tli- Duffing v&i yeu to phi tuyen b~c ba. ky tfnh theo phuang phap ti~m c~n va phuang phap can b~ng dieu hoa duqc so sanh v&i chu ky chinh xac. Nh~n thay ket quit thu duqc tl'r phuang phap can b~ng dieu hoa dtrqc chap nh~n trong khi phuang phap ti~m c~n - nhu da biet - chi c6 the ap cho cac dao d(mg .