TY - GEN
T1 - Nonlinear interaction of a parametrically-excited coupled column-pendulum oscillator
AU - Mustafa, G.
AU - Ertas, A.
N1 - Publisher Copyright:
© 1993 American Society of Mechanical Engineers (ASME). All rights reserved.
PY - 1993
Y1 - 1993
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85104184190&partnerID=8YFLogxK
U2 - 10.1115/DETC1993-0134
DO - 10.1115/DETC1993-0134
M3 - Conference contribution
AN - SCOPUS:85104184190
T3 - Proceedings of the ASME Design Engineering Technical Conference
SP - 447
EP - 453
BT - 14th Biennial Conference on Mechanical Vibration and Noise
PB - American Society of Mechanical Engineers (ASME)
T2 - ASME 1993 Design Technical Conferences, DETC 1993
Y2 - 19 September 1993 through 22 September 1993
ER -