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Effect of nonlinear stiffness on the motion of a flexible pendulum. (English) Zbl 1050.70014
The authors consider a system with two degrees of freedom – a flexible pendulum subjected to harmonic forcing. The system is a mass on spring moving along a rod pivoted at one end, and subject to an external harmonic force. The force exerted by the spring is considered to be \(ax+bx^3\), and the equations of motion are integrated numerically. Three types of spring are studied: a linear spring \((b=0)\); a weakly nonlinear spring, and a strongly nonlinear spring. Results for the frequency portrait and Poincaré section are shown in hodograph form in figures, and the progress from periodic to quasi-periodic motion and then to chaotic motion is clearly shown.

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