A SIMPLE CRITERION FOR ESTABLISHING AN UPPER LIMIT TO THE HARMONIC EXCITATION-LEVEL OF THE DUFFING OSCILLATOR USING THE VOLTERRA SERIES

Higher order frequency response functions, based on the Volterra serie s, are employed to represent the input-output characteristics of the D uffing oscillator subject to sinusoidal excitation. From these a serie s representation of a first order frequency response function of the n on-linear system is obtained and used to derive a simple criterion whi ch 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 cri terion strictly applies only to the Duffing oscillator, the procedure can be applied generally and is extended to a two-degree-of-freedom sy stem with a non-linear cubic stiffness producing a similar criterion t o that of the single degree-of-freedom system. (C) 1996 Academic Press Limited