Superharmonic Resonances of Parametricly Excited Gear System Solved by Homotopy Analysis Method
نویسندگان
چکیده
An analytical technique, namely the homotopy analysis method (HAM), is applied to solve periodic solutions for superharmonic resonances of nonlinear oscillations with parametric excitation. Unlike perturbation methods, HAM does not depend on any small physical parameters at all. Thus, it is valid for both weakly and strongly nonlinear problems. Besides, different from all other analytic techniques, the HAM provides us a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter h. In this paper, periodic analytic approximations for superharmonic resonances of nonlinear oscillations with parametric excitation are obtained by using the HAM, which agree well with numerical results. This article shows that the HAM is a powerful and effective technique for nonlinear dynamical systems.
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