An Experimental Investigation of the Motion of Flexible Strings: Whirling

Whirling of strings has been studied both theoretically and experimentally for many decades. According to linear theory, a heavy string can exhibit steady-state whirl only at its natural frequencies which form a discrete spectrum. The nonlinear theory, however, suggests that a string can undergo steady whirl at any frequency larger than the fundamental frequency and further that for each frequency between the $nth$ and the $(n+1)th$ eigenvalue, there exist $n$ distinct whirling modes. Quantitative experimental observations on such whirling have never been reported, although anecdotal evidence suggests the possibility of such whirl. In this paper, we examine the whirling of a string with negligible bending stiffness through experiments utilizing a stereo-vision imaging system. It is shown that steady motion exists only when the string whirls at its natural frequencies and that whirling motions for other frequencies exhibit rich dynamics that needs further exploration.