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String vibrating at finite amplitude

Published online by Cambridge University Press:  09 April 2009

I. M. Stuart
I. M. Stuart
Affiliation:
Division of Textile Physics C.S.I.R.O. Wool Research Laboratories Ryde, Sydney
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Summary

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Equations of motion of a vibrating string are established in terms of the transverse and longitudinal displacements. These equations contain the terms of lowest order which are neglected in the classical treatment with vanishing amplitude. These extra terms lead to the natural modes being dependent on amplitude. By a simple procedure a solution of these equations is obtained which separates, as in the classical theory. The familiar circular functions are replaced by a Mathiew Function of position and a Jacobi elliptic function of time. Agreement with a previous study is shown.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 6 , Issue 3 , August 1966 , pp. 369 - 384
Copyright
Copyright © Australian Mathematical Society 1966

References

[1]Carrier, G. F., ‘On the non-linear vibration problem of the elastic string’, Quarterly of Applied Mathematics, 3 (1945), 157.CrossRefGoogle Scholar
[2]Carrier, G. F., ‘A note on the vibrating string’, Quarterly of Applied Mathematics, 7 (1949), 97.CrossRefGoogle Scholar
[3]McLachlan, N. W., Theory and application of Mathiew functions (Oxford, 1947).Google Scholar
[4]Byrd, and Friedman, , Handbook of elliptic integrals for engineers and scientists (Heidelberg, 1954).CrossRefGoogle Scholar
[5]Stuart, I. M., ‘Amplitude corrections for vibroscope measurements’, British Journal of Applied Physics, 10 (1959), 219–225.CrossRefGoogle Scholar