Linear control strategies for damping of flexible structures

Starting from the two-component representation technique for damping of structures the possible increase in damping efficiency obtained by introducing collocated active damping is illustrated. The two-component representation of the damped vibration mode is constructed as a linear combination of the undamped mode shape and the mode shape obtained by locking the damper. This leads to a simple set of equations of motion, which in the frequency domain gives an accurate solution for the complex-valued natural frequency, and thereby for the modal damping. This solution shows that attainable damping increases with the phase angle of the damper, and that improved damping efficiency thus follows from the ability of an active device to produce a force acting ahead of velocity. Phase lead is equivalent to negative stiffness, and the effect of negative stiffness is illustrated by a radiation condition on a cable. Simple linear filters, with desirable low-pass properties, are presented as simple means for implementing phase lead.

[1]  Leonard Meirovitch,et al.  Dynamics And Control Of Structures , 1990 .

[2]  André Preumont,et al.  ACTIVE TENDON CONTROL OF CABLE-STAYED BRIDGES , 1996 .

[3]  J. L. Fanson,et al.  Positive position feedback control for large space structures , 1990 .

[4]  Gene F. Franklin,et al.  Feedback Control of Dynamic Systems , 1986 .

[5]  Akira Mita,et al.  Active control of the seismic response of structures by combined use of base isolation and absorbing boundaries , 1992 .

[6]  André Preumont,et al.  Amortissement actif des structures câblées: de la théorie à l'implémentation , 2001 .

[7]  Joseph A. Main,et al.  Efficiency and tuning of viscous dampers on discrete systems , 2005 .

[8]  M. Balas,et al.  Feedback control of flexible systems , 1978 .

[9]  André Preumont,et al.  Vibration Control of Active Structures: An Introduction , 2018 .

[10]  T. K. Caughey,et al.  On the stability problem caused by finite actuator dynamics in the collocated control of large space structures , 1985 .

[11]  C. Mei,et al.  The Analysis and Control of Longitudinal Vibrations from Wave Viewpoint , 2002 .

[12]  Steen Krenk,et al.  Frequency Analysis of the Tuned Mass Damper , 2005 .

[13]  Søren Nielsen,et al.  Vibrations of a shallow cable with a viscous damper , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[14]  T. T. Soong,et al.  Passive Energy Dissipation Systems in Structural Engineering , 1997 .

[15]  R. W. Jones,et al.  Feedback control of flexural waves in beams , 1996 .

[16]  S. Krenk.  Vibrations of a Taut Cable With an External Damper , 2000 .

[17]  M. Balas.  Direct Velocity Feedback Control of Large Space Structures , 1979 .

[18]  Eunsup Sim,et al.  ACTIVE VIBRATION CONTROL OF FLEXIBLE STRUCTURES WITH ACCELERATION FEEDBACK , 1993 .

[19]  S. Krenk.  Complex modes and frequencies in damped structural vibrations , 2004 .