Asymmetrical effects and higher harmonics from nonlinear interactions in a driven vibrating wire

Abstract

Inclusion of tensional changes and longitudinal motion result in coupled nonlinear equations for motion in, and perpendicular to, the plane of the driving force on a stretched wire. Earlier experimental measurements of nonlinear effects in a sinusoidally driven vibrating wire [Hanson et al., J. Acoust. Soc. Am. 96, 1549–1556 (1994)] will be briefly reviewed. Presented data will show that the onset of motion perpendicular to the plane of the driving force depends very sensitively on asymmetries which produce slight differences in free vibration frequencies in two orthogonal directions. Also reported will be results of amplitude and phase measurements of generated second, third, and fourth harmonics of the driving frequency, both in the plane of the driving force (vertical) and perpendicular to it. These higher harmonics, not significant at frequencies far off-resonance, become very significant near a resonance. With the wire driven at frequencies near its third natural resonance, a very pronounced subharmonic splitting of order three has been observed. Qualitative aspects will be illustrated on video tape.