Stability of discretized elastic columns with periodic retarded follower forces

Eric Butcher, Haitao Ma

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

Abstract

The objective of this work is to present a stability analysis for discretized elastic columns under the influence of periodically-varying nonconservative follower forces whose follower angle is retarded, i.e., depends on a previous position of the system. One- and two-degree-of-freedom systems under the simultaneous influence of both parametric excitation and time-delay, whose effects on such systems have previously been studied separately, are considered. By employing an orthogonal polynomial approximation, the so-called "infinite-dimensional Floquet transition matrix" associated with the time-periodic differential-delay system is approximated. The stability criteria that all the eigenvalues (Floquet multipliers) of this matrix must lie within the unit circle is then applied. The stability charts for different combinations of the remaining system parameters are shown, and the previously-reported results for the special cases where either the parametric excitation or the time-delay vanishes are verified. Two cases, when the parametric forcing period is equal to or twice the delay period are taken into consideration in this work.

Original languageEnglish (US)
Title of host publicationProceedings of the Tenth International Congress on Sound and Vibration
EditorsA. Nilson, H. Boden
Pages1587-1594
Number of pages8
StatePublished - 2003
Externally publishedYes
EventProceedings of the Tenth International Congress on Sound and Vibration - Stockholm, Sweden
Duration: Jul 7 2003Jul 10 2003

Other

OtherProceedings of the Tenth International Congress on Sound and Vibration
CountrySweden
CityStockholm
Period7/7/037/10/03

Fingerprint

Time delay
Polynomial approximation
Stability criteria

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Butcher, E., & Ma, H. (2003). Stability of discretized elastic columns with periodic retarded follower forces. In A. Nilson, & H. Boden (Eds.), Proceedings of the Tenth International Congress on Sound and Vibration (pp. 1587-1594)

Stability of discretized elastic columns with periodic retarded follower forces. / Butcher, Eric; Ma, Haitao.

Proceedings of the Tenth International Congress on Sound and Vibration. ed. / A. Nilson; H. Boden. 2003. p. 1587-1594.

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

Butcher, E & Ma, H 2003, Stability of discretized elastic columns with periodic retarded follower forces. in A Nilson & H Boden (eds), Proceedings of the Tenth International Congress on Sound and Vibration. pp. 1587-1594, Proceedings of the Tenth International Congress on Sound and Vibration, Stockholm, Sweden, 7/7/03.
Butcher E, Ma H. Stability of discretized elastic columns with periodic retarded follower forces. In Nilson A, Boden H, editors, Proceedings of the Tenth International Congress on Sound and Vibration. 2003. p. 1587-1594
Butcher, Eric ; Ma, Haitao. / Stability of discretized elastic columns with periodic retarded follower forces. Proceedings of the Tenth International Congress on Sound and Vibration. editor / A. Nilson ; H. Boden. 2003. pp. 1587-1594
@inproceedings{1946930d3db04e4284f40d6f4c1403e7,
title = "Stability of discretized elastic columns with periodic retarded follower forces",
abstract = "The objective of this work is to present a stability analysis for discretized elastic columns under the influence of periodically-varying nonconservative follower forces whose follower angle is retarded, i.e., depends on a previous position of the system. One- and two-degree-of-freedom systems under the simultaneous influence of both parametric excitation and time-delay, whose effects on such systems have previously been studied separately, are considered. By employing an orthogonal polynomial approximation, the so-called {"}infinite-dimensional Floquet transition matrix{"} associated with the time-periodic differential-delay system is approximated. The stability criteria that all the eigenvalues (Floquet multipliers) of this matrix must lie within the unit circle is then applied. The stability charts for different combinations of the remaining system parameters are shown, and the previously-reported results for the special cases where either the parametric excitation or the time-delay vanishes are verified. Two cases, when the parametric forcing period is equal to or twice the delay period are taken into consideration in this work.",
author = "Eric Butcher and Haitao Ma",
year = "2003",
language = "English (US)",
pages = "1587--1594",
editor = "A. Nilson and H. Boden",
booktitle = "Proceedings of the Tenth International Congress on Sound and Vibration",

}

TY - GEN

T1 - Stability of discretized elastic columns with periodic retarded follower forces

AU - Butcher, Eric

AU - Ma, Haitao

PY - 2003

Y1 - 2003

N2 - The objective of this work is to present a stability analysis for discretized elastic columns under the influence of periodically-varying nonconservative follower forces whose follower angle is retarded, i.e., depends on a previous position of the system. One- and two-degree-of-freedom systems under the simultaneous influence of both parametric excitation and time-delay, whose effects on such systems have previously been studied separately, are considered. By employing an orthogonal polynomial approximation, the so-called "infinite-dimensional Floquet transition matrix" associated with the time-periodic differential-delay system is approximated. The stability criteria that all the eigenvalues (Floquet multipliers) of this matrix must lie within the unit circle is then applied. The stability charts for different combinations of the remaining system parameters are shown, and the previously-reported results for the special cases where either the parametric excitation or the time-delay vanishes are verified. Two cases, when the parametric forcing period is equal to or twice the delay period are taken into consideration in this work.

AB - The objective of this work is to present a stability analysis for discretized elastic columns under the influence of periodically-varying nonconservative follower forces whose follower angle is retarded, i.e., depends on a previous position of the system. One- and two-degree-of-freedom systems under the simultaneous influence of both parametric excitation and time-delay, whose effects on such systems have previously been studied separately, are considered. By employing an orthogonal polynomial approximation, the so-called "infinite-dimensional Floquet transition matrix" associated with the time-periodic differential-delay system is approximated. The stability criteria that all the eigenvalues (Floquet multipliers) of this matrix must lie within the unit circle is then applied. The stability charts for different combinations of the remaining system parameters are shown, and the previously-reported results for the special cases where either the parametric excitation or the time-delay vanishes are verified. Two cases, when the parametric forcing period is equal to or twice the delay period are taken into consideration in this work.

UR - http://www.scopus.com/inward/record.url?scp=2342421107&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2342421107&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:2342421107

SP - 1587

EP - 1594

BT - Proceedings of the Tenth International Congress on Sound and Vibration

A2 - Nilson, A.

A2 - Boden, H.

ER -