DYNAMICS OF A STRETCHED STRING WITH A MOVING END

Abstract eng:
The response of a string with an axially oscillating end support was investigated analytically. The assumed modes method was used to convert the original continuous system into a series of Hill’s equations. First order approximate solutions were obtained using the method of averaging. The impact of the natural frequencies of vibration of the unperturbed system being commensurate was also examined. The transition curves, separating regions of stability and instability, were determined for even and odd combination resonances of the frequency of the axially oscillating end. The influence of the amplitude and frequency of the oscillation of the moving support was discussed.

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