Non-linear vibration of an elastic string

Narasimha, R. (1968) Non-linear vibration of an elastic string Journal of Sound and Vibration, 8 (1). pp. 134-146. ISSN 0022-460X

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Equations proposed in previous work on the non-linear motion of a string show a basic disagreement, which is here traced to an assumption about the longitudinal displacement u. It is shown that it is neither necessary nor justifiable to assume that u is zero; and also that the velocity of propagation of u disturbances in a string is different from that in an infinite medium, although this difference is usually negligible. After formulating the exact equations of motion for the string, a systematic procedure is described for obtaining approximations to these equations to any order, making only the assumption that the strain in the material of the string is small. The lowest order equations in this scheme are non-linear, and are used to describe the response of a string near resonance. Finally, it is shown that in the absence of damping, planar motion of a string is always unstable at sufficiently high amplitudes, the critical amplitude falling to zero at the natural frequency and its subharmonics. The effect of slight damping on this instability is also discussed.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
ID Code:24589
Deposited On:29 Nov 2010 08:43
Last Modified:09 Jun 2011 09:41

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