Affordable Access

Publisher Website

Resonant dynamics of an autoparametric system: A study using higher-order averaging

International Journal of Non-Linear Mechanics
Publication Date
DOI: 10.1016/0020-7462(95)00041-0


Abstract The autoparametric system consisting of a pendulum attached to a primary spring-mass is known to exhibit 1:2 internal resonance, and amplitude-modulated chaos under harmonic forcing conditions. First-order averaging studies and an analysis of the amplitude dynamics predicts that the response curves of the system exhibit saturation. The period-doubling route to chaos is observed following a Hopf bifurcation to limit cycles. However, to answer questions about the range of the small parameter ε (a function of the forcing amplitude) for which the solutions are valid, and about the persistence of some unstable dynamical behavior, like saturation, higher-order non-linear effects need to be taken into account. Second-order averaging of the system is undertaken to address these issues. Loss of saturation is observed in the steady-state amplitude responses. The breaking of symmetry in the various bifurcation sets becomes apparent as a consequence of ε appearing in the averaged equations. For larger ε, second-order averaging predicts additional Pitchfork and Hopf bifurcation points in the single-mode response. For the response between the two Hopf bifurcation points from the coupled-mode solution branch, the period-doubling as well as the Silnikov mechanism for chaos are observed. The predictions of the averaged equations are verified qualitatively for the original equations.

There are no comments yet on this publication. Be the first to share your thoughts.


Seen <100 times

More articles like this

Higher-order averaging schemes in systems with fas...

on Journal of Applied Mathematics... Jan 01, 2002

A note on higher order averaging

on International Journal of Non-L... Jan 01, 1988

Higher-order averaging: periodic solutions, linear...

on Nonlinear Analysis Theory Meth... Jan 01, 2003
More articles like this..