Nonlinear interaction of a parametrically-excited coupled column-pendulum oscillator

G. Mustafa, A. Ertas

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


A new vibration absorbing device is introduced for large flexible structures. The bifurcation diagrams obtained for the averaged system, indicate that the system loses stability via two distinct routes. One leading to a saddle-node bifurcation, normally associated with the jump phenomena. The second instability is due to the Hopf bifurcation, that results in amplitude modulated motion of the oscillator. A parameter range has been identifled where these bifurcations coalesce. This phenomenon is a strong indicator of existence of homoclinic orbits. In addition to the regular solution branches, that bifurcate from the zero solution, the system also possesses isolated solutions (the so-called” isolas”) that form isolated loops bounded away horn zero. As the forcing amplitude is varied, the isolas appear, disappear or coalesce with the regular solution branches.The response curves indicate that the column amplitude shows saturation. The pendulum acts as a vibration absorber over a range of frequency where the column response is saturated. However, there is also a frequency range over which a reverse flow of energy occurs, where the pendulum shows reduced amplitude at the cost of large amplitudes of the column.

Original languageEnglish
Title of host publication14th Biennial Conference on Mechanical Vibration and Noise
Subtitle of host publicationDynamics and Vibration of Time-Varying Systems and Structures
PublisherAmerican Society of Mechanical Engineers (ASME)
Number of pages7
ISBN (Electronic)9780791811733
StatePublished - 1993
EventASME 1993 Design Technical Conferences, DETC 1993 - Albuquerque, United States
Duration: Sep 19 1993Sep 22 1993

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
VolumePart F167972-5


ConferenceASME 1993 Design Technical Conferences, DETC 1993
Country/TerritoryUnited States


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