Stability of elastic columns with periodic retarded follower forces

Haitao Ma, Eric Butcher

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

The objective of this work is to present a stability analysis for elastic columns under the influence of periodically varying follower forces whose orientation is retarded, i.e., depends on the position of the system at a previous time. One- and two-degree-of-freedom (dof) discretized systems under the simultaneous influence of both parametric excitation and time-delay, whose effects on such systems have previously been only considered separately, are studied. By employing an orthogonal polynomial approximation, the 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. For special cases of the single dof system, the numerical stability plots are verified by considering the analytical expressions for the corresponding stability boundaries for an analogous delayed Mathieu equation.

Original languageEnglish (US)
Pages (from-to)849-867
Number of pages19
JournalJournal of Sound and Vibration
Volume286
Issue number4-5
DOIs
StatePublished - Sep 22 2005
Externally publishedYes

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Time delay
Polynomial approximation
time lag
degrees of freedom
Convergence of numerical methods
Stability criteria
Mathieu function
numerical stability
multipliers
charts
excitation
polynomials
eigenvalues
plots
matrices
approximation

ASJC Scopus subject areas

  • Engineering(all)
  • Mechanical Engineering

Cite this

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

In: Journal of Sound and Vibration, Vol. 286, No. 4-5, 22.09.2005, p. 849-867.

Research output: Contribution to journalArticle

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