Parameters Approach Applied on Nonlinear Oscillators

Abstract EN

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.