Parametric resonance and nonlinear string vibrations

Rowland, David R. (2004) Parametric resonance and nonlinear string vibrations. American Journal of Physics, 72 6: 758-766. doi:10.1119/1.1645281


Author Rowland, David R.
Title Parametric resonance and nonlinear string vibrations
Journal name American Journal of Physics   Check publisher's open access policy
ISSN 0002-9505
Publication date 2004-06
Sub-type Article (original research)
DOI 10.1119/1.1645281
Volume 72
Issue 6
Start page 758
End page 766
Total pages 9
Editor J. Tobochnik
Place of publication Lancaster, Pa., U.S.A.
Publisher American Association of Physics Teachers
Collection year 2004
Language eng
Subject C1
02 Physical Sciences
Formatted abstract
Periodic changes in the tension of a taut string parametrically excite transverse motion in the string when the driving frequency is close to twice the natural frequency of any transverse normal mode of the string. The literature on this phenomenon is synthesized and extended to include the effects of damping as well as nonlinearity. It is shown that it is nonlinearity rather than damping that limits the growth of a resonantly excited mode, although damping is needed for steady-state oscillations to occur. The validity of the usual approximation that the string tension depends only on time and not on space is checked by modeling a string as point masses joined by massless linear springs. It is found that although this approximation is likely to be violated in practice, the violation does not have a significant effect on the results. The source of the disagreement in the literature for the speed of longitudinal waves in a stretched string is identified.
©2004 American Association of Physics Teachers.
Keyword Physics education
Young's modulus
Mathieu equation
Vibrations
Teaching
Nonlinear equations
Damping
Oscillations
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
2005 Higher Education Research Data Collection
 
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Citation counts: TR Web of Science Citation Count  Cited 19 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 21 times in Scopus Article | Citations
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Created: Wed, 15 Aug 2007, 05:20:35 EST