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On a Problem of Large-Amplitude Oscillation of a Non-linear Conservative System with Inertia and Static Non-linearity |
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PP: 173-183 |
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Author(s) |
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G. M. Abd El-Latif,
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Abstract |
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| In this paper we will study the non-linear oscillation of a conservative system having
inertia and static non-linearities. By combining the linearization of the governing
equation with the method of harmonic balance, we investigate analytical approximate
solutions for the non-linear oscillations of the system. Unlike the classical harmonic
balance method, linearization is performed prior to proceeding with harmonic balancing,
thus resulting in a set of linear algebraic equations instead of one of non-linear
algebraic equations. Hence, we are able to establish analytical approximate formulas
for the exact frequency and periodic solution. These analytical approximate formulas
show excellent agreement with the exact solutions, and are valid for small as well as
large amplitudes of oscillation. |
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