Theory and Experiment on Establishing the Stability Boundaries of a One Degree of Freedom System Under Two High Frequency Parametric Excitation Inputs

R. J. Yatawara, Richard David Neilson, A. D. S. Barr

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The stability of a single-degree-of-freedom linear system to two high-frequency parametric inputs is considered. Equations defining approximately the stability boundaries of the system are developed using Struble's method. The results of the analysis for a range of input frequency ratios and input amplitudes are compared with exact solutions for the regions of instability calculated from the monodromy matrix. Good agreement is found for low excitation levels. Experimental work involving the small amplitude oscillation of a pendulum under two frequency parametric motion is described, instability zones are found to exist and their stability boundaries shown to be reasonably close to those derived from the theory. (c) 2006 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)962-980
Number of pages18
JournalJournal of Sound and Vibration
Volume297
Issue number3-5
DOIs
Publication statusPublished - Nov 2006

Keywords

  • OSCILLATOR
  • PENDULUM

Cite this

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title = "Theory and Experiment on Establishing the Stability Boundaries of a One Degree of Freedom System Under Two High Frequency Parametric Excitation Inputs",
abstract = "The stability of a single-degree-of-freedom linear system to two high-frequency parametric inputs is considered. Equations defining approximately the stability boundaries of the system are developed using Struble's method. The results of the analysis for a range of input frequency ratios and input amplitudes are compared with exact solutions for the regions of instability calculated from the monodromy matrix. Good agreement is found for low excitation levels. Experimental work involving the small amplitude oscillation of a pendulum under two frequency parametric motion is described, instability zones are found to exist and their stability boundaries shown to be reasonably close to those derived from the theory. (c) 2006 Elsevier Ltd. All rights reserved.",
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author = "Yatawara, {R. J.} and Neilson, {Richard David} and Barr, {A. D. S.}",
year = "2006",
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journal = "Journal of Sound and Vibration",
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TY - JOUR

T1 - Theory and Experiment on Establishing the Stability Boundaries of a One Degree of Freedom System Under Two High Frequency Parametric Excitation Inputs

AU - Yatawara, R. J.

AU - Neilson, Richard David

AU - Barr, A. D. S.

PY - 2006/11

Y1 - 2006/11

N2 - The stability of a single-degree-of-freedom linear system to two high-frequency parametric inputs is considered. Equations defining approximately the stability boundaries of the system are developed using Struble's method. The results of the analysis for a range of input frequency ratios and input amplitudes are compared with exact solutions for the regions of instability calculated from the monodromy matrix. Good agreement is found for low excitation levels. Experimental work involving the small amplitude oscillation of a pendulum under two frequency parametric motion is described, instability zones are found to exist and their stability boundaries shown to be reasonably close to those derived from the theory. (c) 2006 Elsevier Ltd. All rights reserved.

AB - The stability of a single-degree-of-freedom linear system to two high-frequency parametric inputs is considered. Equations defining approximately the stability boundaries of the system are developed using Struble's method. The results of the analysis for a range of input frequency ratios and input amplitudes are compared with exact solutions for the regions of instability calculated from the monodromy matrix. Good agreement is found for low excitation levels. Experimental work involving the small amplitude oscillation of a pendulum under two frequency parametric motion is described, instability zones are found to exist and their stability boundaries shown to be reasonably close to those derived from the theory. (c) 2006 Elsevier Ltd. All rights reserved.

KW - OSCILLATOR

KW - PENDULUM

U2 - 10.1016/j.jsv.2006.05.008

DO - 10.1016/j.jsv.2006.05.008

M3 - Article

VL - 297

SP - 962

EP - 980

JO - Journal of Sound and Vibration

JF - Journal of Sound and Vibration

SN - 0022-460X

IS - 3-5

ER -