2126. Parameter-induced fractal erosion of the safe basin in a softening Duffing oscillator
School of Mechatronic Engineering, China
University of Mining and Technology,
Jiangsu Key Laboratory of Mine Mechanical and
Received 26 May 2016; received in revised form 11 July 2016; accepted 18 July 2016
Abstract. The parameter-induced fractal erosion of the safe basin is investigated in a softening Duffing system. For a fixed excitation, we make the linear stiffness, the nonlinear stiffness and the damping coefficient as the control parameter. At first, the necessary condition for the fractal erosion of the safe basin is obtained by the Melnikov method. Then, the analytical predications are verified by the numerical simulations. With the variation of the stiffness or the damping coefficient, the fractal erosion of the safe basin will appear or vanish. Both the linear and the nonlinear stiffness influence the topology of the safe basin. With the increase of the linear stiffness, the fractal erosion of the safe basin will appear at first and then disappear gradually. The area of the safe basin is an increasing function of the linear stiffness. With the increase of the nonlinear stiffness, the fractal erosion of the safe basin appears and the area of the safe basin turns smaller. The topology of the safe basin is independent of the damping coefficient. For small damping coefficient, the fractal erosion of the safe basin occurs much more easily. The damping coefficient suppresses the fractal erosion of the safe basin.
Keywords: safe basin erosion, fractal, chaos, Melnikov integral.
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Cite this article
Yang Shanguo Parameter‑induced fractal erosion of the safe basin in a softening Duffing oscillator. Journal of Vibroengineering, Vol. 18, Issue 5, 2016, p. 3329‑3336.
© JVE International Ltd. Journal of Vibroengineering. Aug 2016, Vol. 18, Issue 5. ISSN 1392-8716