A SIMPLE CRITERION FOR ESTABLISHING AN UPPER LIMIT TO THE HARMONIC EXCITATION LEVEL OF THE DUFFING OSCILLATOR USING THE VOLTERRA SERIES - Tomlinson, G.R.; Manson, G.; Lee, G.M. (Journal of sound and vibration, 1996)
High order frequency response functions, based on the Volterra series, are employed to represent the input-output characteristics of the Duffing oscillator subject to sinusoidal excitation. From these a series representation of a first order frequency response function of the non-linear system is obtained and used to derive a simple criterion which provides an estimate of the magnitude of the input sine-wave above which the predicted response begins to diverge. The criterion results in a small overestimate of the magnitude of the input force excitation at the undamped natural frequency condition. Although the derived criterion strictly applies only to the Duffing oscillator, the procedure can be applied generally and is extended to a two-degree-of-freedom system with a non-linear cubic stiffness producing a similar criterion to that of the single degree-of-freedom system.