Asymptotic analysis of weakly nonlinear and forced oscillations

Abstract

The restriction ofK-B averaging method is discussed and asymptotic solution of the weakly nonlinear and forced oscillationu″+ω₀²u=εkcosωt−εu³ is obtained by Struble technique. The conclusion about this oscillation derived with other method is discussed. The results show thatK-B method will break down whena andθ in the zeroth solution of above eqation are not slowly varying functions of timet. The stationary solution of weakly nonlinear oscillation,u″+ω₀²u=εkcosω(ε)t-εu³ is also analysed.

Keywords

asymptotic analysis / forced oscillation / perturbation method

References

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