Stability Boundaries of Period-1 Rotation for a Pendulum Under Combined Vertical and Horizontal Excitation

Bryan Horton, S. Lenci, Ekaterina Pavlovskaia, F. Romeo, G. Rega, Marian Wiercigroch

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The aim of this work is to study the dynamics of pendulum driven through its pivot moving in both horizontal and vertical directions. It expands the results obtained for the parametric pendulum by Lenci et al. to two other cases, i.e. the elliptically excited pendulum and the pendulum, with an inclined rectilinear base motion (the tilted pendulum). Here we derive approximate analytical expressions representing the position of the saddle-node bifurcation associated with period-1 rotations in the excitation amplitude/frequency plane in the presence of damping by using the perturbation method proposed by Lenci et al. This includes development of a procedure for deducing expressions for the period doubling, creating a pair of stable period-2 rotational attractors. The obtained approximations are plotted on the excitation parameters plane and compared with numerical results. Simple Pad´e approximations for the analytical expressions relating to the position of the saddle-node bifurcation are also obtained.
Original languageEnglish
Pages (from-to)103–126
Number of pages24
JournalJournal of Applied Nonlinear Dynamics
Volume2
Issue number2
DOIs
Publication statusPublished - Apr 2013

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