Out-of-Plane Motion of a Stretched String under Forced Vibration

Abstract

This paper treats the nonlinear phenomenon of out-of-plane motion that may develop under certain conditions in a stretched string subjected to planar forced vibrations. As in a previous paper dealing with the case of in-plane motion [J. Acoust. Soc. Am. (Dec. 1960)], the lack of inertial effects for longitudinal deformations occuring during transverse vibrations leads to tension levels that are uniform along the string but varying in time, and separable solutions are seen to result. In the course of the discussion, the out-of-plane motion is analyzed in terms of stability diagrams of Mathieu's equation, and results provide an interpretation of two types of out-plane motion, a “jump rope” mode (out of plane component 90° out of phase with in-plane component) and a “warped plane” mode (out of plane component in phase) which have been observed in experiments involving a slotted end constraint on the string. In the oral presentation, a motion picture sequence illustrating the characteristics of transverse vibration in an actual vibrating string will be presented.