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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.

##### MSC:
 70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics 70K50 Bifurcations and instability for nonlinear problems in mechanics 70K40 Forced motions for nonlinear problems in mechanics
##### Keywords:
mass on spring; harmonic forcing; Poincaré section
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