TY - JOUR
T1 - Stability of elastic columns with periodic retarded follower forces
AU - Ma, Haitao
AU - Butcher, Eric A.
N1 - Funding Information:
This paper is based upon work supported by the National Science Foundation under Grant No. 0114500.
PY - 2005/9/22
Y1 - 2005/9/22
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jsv.2004.10.052
DO - 10.1016/j.jsv.2004.10.052
M3 - Article
AN - SCOPUS:22344437802
SN - 0022-460X
VL - 286
SP - 849
EP - 867
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
IS - 4-5
ER -