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Parameters Approach Applied on Nonlinear Oscillators
Parameters Approach Applied on Nonlinear Oscillators
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Parameters Approach Applied on Nonlinear Oscillators
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Parameters Approach Applied on Nonlinear Oscillators
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Parameters Approach Applied on Nonlinear Oscillators
Parameters Approach Applied on Nonlinear Oscillators
Journal Article

Parameters Approach Applied on Nonlinear Oscillators

2014
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Overview
We applied an approach to obtain the natural frequency of the generalized Duffing oscillator u ¨ + u + α 3 u 3 + α 5 u 5 + α 7 u 7 + ⋯ + α n u n = 0 and a nonlinear oscillator with a restoring force which is the function of a noninteger power exponent of deflection u ¨ + α u | u | n − 1 = 0 . This approach is based on involved parameters, initial conditions, and collocation points. For any arbitrary power of n , the approximate frequency analysis is carried out between the natural frequency and amplitude. The solution procedure is simple, and the results obtained are valid for the whole solution domain.