Axial force stabilization of transverse beam vibration

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)

Abstract

An axial force stabilizes the transverse vibration of a beam with translational and rotational boundary springs and arbitrary geometry. The nonlinearly coupled , longitudinal and transverse equations of motion of the beam with axial force control are derived and simplified using a quasistatic assumption. Lyapunov's direct method and an invariance principle for distributed systems show that an axial damper can asymptotically and simultaneously stabilize all transverse vibration modes. Asymptotic stability is guaranteed if the eigenvalues are simple and nonzero and if there are no internal resonances between coupled modes.

Original languageEnglish (US)
Title of host publicationVibration and Control of Mechanical Systems
PublisherPubl by ASME
Pages29-34
Number of pages6
Volume61
ISBN (Print)0791811778
StatePublished - 1993
EventProceedings of the 14th Biennial ASME Design Technical Conference on Mechanical Vibration and Noise - Albuquerque, NM, USA
Duration: Sep 19 1993Sep 22 1993

Other

OtherProceedings of the 14th Biennial ASME Design Technical Conference on Mechanical Vibration and Noise
CityAlbuquerque, NM, USA
Period9/19/939/22/93

Fingerprint

Force control
Asymptotic stability
Invariance
Equations of motion
Stabilization
Geometry

All Science Journal Classification (ASJC) codes

  • Engineering(all)

Cite this

Rahn, C. D., & Mote, C. D. (1993). Axial force stabilization of transverse beam vibration. In Vibration and Control of Mechanical Systems (Vol. 61, pp. 29-34). Publ by ASME.
Rahn, Christopher D. ; Mote, C. D. / Axial force stabilization of transverse beam vibration. Vibration and Control of Mechanical Systems. Vol. 61 Publ by ASME, 1993. pp. 29-34
@inproceedings{38e5199a13ac4dc08067bf3650a11cdc,
title = "Axial force stabilization of transverse beam vibration",
abstract = "An axial force stabilizes the transverse vibration of a beam with translational and rotational boundary springs and arbitrary geometry. The nonlinearly coupled , longitudinal and transverse equations of motion of the beam with axial force control are derived and simplified using a quasistatic assumption. Lyapunov's direct method and an invariance principle for distributed systems show that an axial damper can asymptotically and simultaneously stabilize all transverse vibration modes. Asymptotic stability is guaranteed if the eigenvalues are simple and nonzero and if there are no internal resonances between coupled modes.",
author = "Rahn, {Christopher D.} and Mote, {C. D.}",
year = "1993",
language = "English (US)",
isbn = "0791811778",
volume = "61",
pages = "29--34",
booktitle = "Vibration and Control of Mechanical Systems",
publisher = "Publ by ASME",

}

Rahn, CD & Mote, CD 1993, Axial force stabilization of transverse beam vibration. in Vibration and Control of Mechanical Systems. vol. 61, Publ by ASME, pp. 29-34, Proceedings of the 14th Biennial ASME Design Technical Conference on Mechanical Vibration and Noise, Albuquerque, NM, USA, 9/19/93.

Axial force stabilization of transverse beam vibration. / Rahn, Christopher D.; Mote, C. D.

Vibration and Control of Mechanical Systems. Vol. 61 Publ by ASME, 1993. p. 29-34.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - Axial force stabilization of transverse beam vibration

AU - Rahn, Christopher D.

AU - Mote, C. D.

PY - 1993

Y1 - 1993

N2 - An axial force stabilizes the transverse vibration of a beam with translational and rotational boundary springs and arbitrary geometry. The nonlinearly coupled , longitudinal and transverse equations of motion of the beam with axial force control are derived and simplified using a quasistatic assumption. Lyapunov's direct method and an invariance principle for distributed systems show that an axial damper can asymptotically and simultaneously stabilize all transverse vibration modes. Asymptotic stability is guaranteed if the eigenvalues are simple and nonzero and if there are no internal resonances between coupled modes.

AB - An axial force stabilizes the transverse vibration of a beam with translational and rotational boundary springs and arbitrary geometry. The nonlinearly coupled , longitudinal and transverse equations of motion of the beam with axial force control are derived and simplified using a quasistatic assumption. Lyapunov's direct method and an invariance principle for distributed systems show that an axial damper can asymptotically and simultaneously stabilize all transverse vibration modes. Asymptotic stability is guaranteed if the eigenvalues are simple and nonzero and if there are no internal resonances between coupled modes.

UR - http://www.scopus.com/inward/record.url?scp=0027800419&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027800419&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0027800419

SN - 0791811778

VL - 61

SP - 29

EP - 34

BT - Vibration and Control of Mechanical Systems

PB - Publ by ASME

ER -

Rahn CD, Mote CD. Axial force stabilization of transverse beam vibration. In Vibration and Control of Mechanical Systems. Vol. 61. Publ by ASME. 1993. p. 29-34