Analyzing of Nonlinear Generalized Duffing Oscillators Using the Equivalent Linearization Method with a Weighted Averaging
D. V. Hieu *
Department of Mechanics, Thai Nguyen University of Technology, Vietnam.
N. Q. Hai
Department of Mathematics, Ha Noi Architectural University, Vietnam.
*Author to whom correspondence should be addressed.
Abstract
The generalized Duffing oscillator is investigated in this paper by using the Equivalent Linearization method with a weighted averaging. Applying of the Equivalent Linearization method in which the averaging value is calculated in a new way called the weighted averaging value by introducing a weighted coefficient function, the amplitude-frequency relationship of the oscillator is obtained in a closed-form. The obtained solutions have been compared with approximate analytical solutions, exact solutions and numerical solutions. Comparisons show the reliability of the present solutions.
Keywords: Equivalent linearization method, weighted averaging, generalized Duffing, nonlinear oscillator.