Autoresonance in a pair of coupled oscillators
We investigate passage through resonance in a two-degree of freedom system consisting of a linear oscillator weakly coupled to a nonlinear forced actuator. Two classes of problems are studied analytically and numerically: (1) a periodic force with constant frequency is applied to the nonlinear actuator (the Duffing oscillator) with slowly time-decreasing linear stiffness; (2)
the time-invariant nonlinear oscillator is excited by a force with slowly increasing frequency. In both cases, the attached linear oscillator and linear coupling remain time-invariant, and the system is initially engaged in resonance. This paper demonstrates that in the systems of the first type autoresonance (AR) occurs in both oscillators. In the system of the second type AR occurs only in the excited nonlinear oscillator but the coupled linear oscillator exhibits small bounded oscillations. Assuming a slow change of detuning rate, we obtain explicit asymptotic approximations for the amplitudes and the phases of oscillations close to exact (numerical) results.
CYBERNETICS AND PHYSICS, Vol. 3, No. 4. 2014, 166-173.