Abstract
In this paper, the existence of chaotic behavior in the single-well Duffing Oscillator was examined under parametric excitations using Melnikov method and Lyapunov exponents. The minimum and maximum values were obtained and the dynamical behaviors showed the intersections of manifold which was illustrated using the MATCAD software. This extends some results in the literature. Simulation results indicate that the single-well oscillator is sensitive to sinusoidal signals in high frequency cases and with high damping factor, the amplitude of the oscillator was reduced.
Highlights
Duffing oscillators have received remarkable attention in the recent decades due to the variety of their Engineering applications, for example magneto-elastic mechanical system [1], large amplitude oscillator of centrifugal governing system [2], nonlinear vibration beans and plates [3] [4] and fluid flow induced vibration [5]
The existence of chaotic behavior in the single-well Duffing Oscillator was examined under parametric excitations using Melnikov method and Lyapunov exponents
Chaos occurs when the behavior of the dynamical system is extremely sensitive to initial conditions
Summary
Duffing oscillators have received remarkable attention in the recent decades due to the variety of their Engineering applications, for example magneto-elastic mechanical system [1], large amplitude oscillator of centrifugal governing system [2], nonlinear vibration beans and plates [3] [4] and fluid flow induced vibration [5]. It is famous for the existence of chaos behavior in recent decades [6]. Various researchers have used different methods in obtaining solutions, for instance, Ueda [7] used the numerical simulation where changes in attractors were obtained under various parameters
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