×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI