Abstract This paper presents a theoretical and experimental study of the resonance phenomena of a nonlinear system, the time dependent part of which is governed by Duffing's equation. The method of Krylov, Bogoliubov and Mitropolsky is applied to analyze the transient motion near resonance, and the amplitude of the system is shown to change rapidly, during a short time duration, at certain critical driving frequencies. During this transitional period, the instantaneous response frequency of the system differs from the driving frequency, and the variation of amplitude vs response frequency is bounded by the usual steady-state nonlinear response curve. Experimental results are presented for a clamped circular plate driven into large amplitude oscillations by a magnetic force, during the downward and upward “jumps”. The transient nonlinear response curves during the jumps, and the free vibration (skelton) curves of the plate are determined experimentally. Methods for measuring the damping coefficient, linear frequency and nonlinear stiffness of the plate are also discussed.
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