NEWTON-HARMONIC BALANCING APPROACH FOR NONLINEAR FREE VIBRATION OF AN ELASTICALLY-RESTRAINED CANTILEVER BEAM
This paper presents a new approach for solving accurate approximate analytical higher-order solutions for strong nonlinear Duffing oscillators with cubic-quintic nonlinear restoring force. The system is conservative and with odd nonlinearity. The new approach couples Newton’s method with harmonic balancing. Unlike the classical harmonic balance method, accurate analytical approximate solutions are possible because linearization of the governing differential equation by Newton’s method is conducted prior to harmonic balancing. The approach yields simple linear algebraic equations instead of nonlinear algebraic equations without analytical solution. Using the approach, accurate higher-order approximate analytical expressions for period and periodic solution are established. These approximate solutions are valid for small as well as large amplitudes of oscillation. In addition, it is not restricted to the presence of a small parameter such as in the classical perturbation method. Illustrative examples are presented to verify accuracy and explicitness of the approximate solutions. The effect of strong quintic nonlinearity on accuracy as compared to cubic nonlinearity is also discussed.
Newtons method Harmonic Balance method Duffing equation
Q.C.Zeng R.Xu Yonghao Huang Huandong Yuan Weiming Peng C.W.Lim
Johnton Science & Technology Group (Hong Kong) Ltd., Kowloon, Hong Kong, P.R.China Department of Building and Construction, City University of Hong Kong, Kowloon, Hong Kong, P.R.China Wuhan Huayi Electronics Co.,Ltd.,Gaoxinliulu, Eastern Lake Hi-tech Development Zone, Wuhan, China 43 Manufacture Technology Department, Dongfang Turbine Co.,Ltd.Deyang, Sichuan, 618201, P.R.China
国际会议
The Fifth International Conference on VETOMAC-V(第五届振动工程及机械技术国际会议)
武汉
英文
578-582
2009-08-27（万方平台首次上网日期，不代表论文的发表时间）