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Application of a modified rational harmonic balance method for a class of strongly nonlinear oscillators. (English) Zbl 1223.34055

Summary: An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the rational harmonic balance method in which analytical approximate solutions have rational form. This approach gives us the frequency of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems with complex nonlinearities.

MSC:

34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
70K20 Stability for nonlinear problems in mechanics
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References:

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