Axial force stabilization of transverse beam vibration

Christopher D. Rahn; C. D. Mote

doi:10.1115/DETC1993-0217

Axial force stabilization of transverse beam vibration

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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 language	English (US)
Title of host publication	14th Biennial Conference on Mechanical Vibration and Noise
Subtitle of host publication	Vibration and Control of Mechanical Systems
Publisher	American Society of Mechanical Engineers (ASME)
Pages	29-34
Number of pages	6
ISBN (Electronic)	9780791811771
DOIs	https://doi.org/10.1115/DETC1993-0217
State	Published - 1993
Event	ASME 1993 Design Technical Conferences, DETC 1993 - Albuquerque, United States Duration: Sep 19 1993 → Sep 22 1993

Publication series

Name	Proceedings of the ASME Design Engineering Technical Conference
Volume	Part F167972-9

Conference

Conference	ASME 1993 Design Technical Conferences, DETC 1993
Country/Territory	United States
City	Albuquerque
Period	9/19/93 → 9/22/93

All Science Journal Classification (ASJC) codes

Mechanical Engineering
Computer Graphics and Computer-Aided Design
Computer Science Applications
Modeling and Simulation

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10.1115/DETC1993-0217

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Rahn, C. D., & Mote, C. D. (1993). Axial force stabilization of transverse beam vibration. In 14th Biennial Conference on Mechanical Vibration and Noise: Vibration and Control of Mechanical Systems (pp. 29-34). (Proceedings of the ASME Design Engineering Technical Conference; Vol. Part F167972-9). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/DETC1993-0217

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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.}",

note = "Publisher Copyright: {\textcopyright} 1993 American Society of Mechanical Engineers (ASME). All rights reserved.; ASME 1993 Design Technical Conferences, DETC 1993 ; Conference date: 19-09-1993 Through 22-09-1993",

year = "1993",

doi = "10.1115/DETC1993-0217",

language = "English (US)",

series = "Proceedings of the ASME Design Engineering Technical Conference",

publisher = "American Society of Mechanical Engineers (ASME)",

pages = "29--34",

booktitle = "14th Biennial Conference on Mechanical Vibration and Noise",

}

Rahn, CD & Mote, CD 1993, Axial force stabilization of transverse beam vibration. in 14th Biennial Conference on Mechanical Vibration and Noise: Vibration and Control of Mechanical Systems. Proceedings of the ASME Design Engineering Technical Conference, vol. Part F167972-9, American Society of Mechanical Engineers (ASME), pp. 29-34, ASME 1993 Design Technical Conferences, DETC 1993, Albuquerque, United States, 9/19/93. https://doi.org/10.1115/DETC1993-0217

Axial force stabilization of transverse beam vibration. / Rahn, Christopher D.; Mote, C. D.
14th Biennial Conference on Mechanical Vibration and Noise: Vibration and Control of Mechanical Systems. American Society of Mechanical Engineers (ASME), 1993. p. 29-34 (Proceedings of the ASME Design Engineering Technical Conference; Vol. Part F167972-9).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AU - Mote, C. D.

PY - 1993

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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.

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ER -

Axial force stabilization of transverse beam vibration

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