Large amplitude primary and superharmonic resonances in the Duffing oscillator

doi:10.1016/S0022-460X(86)80141-9

Journal of Sound and Vibration

Volume 110, Issue 3, 8 November 1986, Pages 363-380

https://doi.org/10.1016/S0022-460X(86)80141-9 Get rights and content

Second order perturbation analyses are presented of the order three superharmonic resonance in a Duffing oscillator, ü+δu˙+u³ = P cos ϯt and of the primary resonance in a Duffing oscillator with softening non-linearity, ü+δu˙-u³ = P cos ϯt. It is found in the former case that it is necessary to go to the second order to obtain realistic steady state stability results. In the latter problem, however, the second order solution gives little or no improvement on the first order result. Also presented, for the latter problem, is what is thought to be the first example of a ȁdouble jumpȁ phenomenon for single degree of freedom, harmonically excited oscillators.

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^Ȃ: Now at Department of Mechanical Engineering, Washington State University, Pullman, Washington 99164-2920, U.S.A.

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Large amplitude primary and superharmonic resonances in the Duffing oscillator

Journal of Sound and Vibration

Applied Mathematical Modelling

International Journal of Non-Linear Mechanics

Journal of Sound and Vibration

Physics Letters

International Journal of Non-Linear Mechanics

International Journal of Non-Linear Mechanics

International Journal of Non-Linear Mechanics

International Journal of Non-Linear Mechanics

Journal of Sound and Vibration

Journal of Sound and Vibration

Steady motions exhibited by Duffing's equation

Randomly transitional phenomena in the system governed by Duffing's equation

Journal of Statistical Physics

Explosion of strange attractors exhibited by Duffing's equation

Annals of the New York Academy of Sciences