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A New Approximate Solution for a Generalized Nonlinear Oscillator

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Abstract

The equivalent linearization method based on weighted averaging is employed to obtain a approximate solution for a generalized nonlinear oscillator given in the form of \( \ddot{u} + \alpha u + \beta u^{m} + \frac{{\gamma u^{n} }}{{\mu + \delta u^{p} }} = 0. \) The amplitude–frequency relationship of oscillation is given in a closed-form. Accuracy of the approximate solution is verified by comparing the obtained solution with the numerical solution using the 4th-order Runge–Kutta method. Specifically, the obtained results for some special cases such as cubic-, quintic-, seventh order-Duffing oscillators, Duffing-harmonic oscillator, nonlinear oscillator with fractional nonlinearity are compared with the results achieved by the other approximate methods.

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Acknowledgements

The research is supported by Thai Nguyen University of Technology Grant for a Scientific Project (No. “T2018-B27”).

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  1. Department of Mechanics, Faculty of Automotive and Power Machinery Engineering, Thai Nguyen University of Technology, Thainguyen, Vietnam

    Dang Van Hieu

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Hieu, D.V. A New Approximate Solution for a Generalized Nonlinear Oscillator. Int. J. Appl. Comput. Math 5, 126 (2019). https://doi.org/10.1007/s40819-019-0709-9

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