Unusual motions due to nonlinear effects in a driven vibrating string

Abstract

Usual nonlinear effects observed in a sinusoidally driven vibrating string include generation of motion perpendicular to the driving plane, sudden jumps of amplitude and associated hysteresis, and generation of higher harmonics. In addition, under some conditions, there can be a rich variety of unusual, very complex motions of a point on the string, the pattern of which, together with associated harmonic (and sometimes subharmonic) content, can change dramatically with a slight change in driving frequency or sometimes with constant driving frequency and force. Intrinsic string asymmetries can also have a profound effect on the behavior. In a brass harpsichord string (wire) such asymmetries can cause a small splitting of each natural frequency of free vibration into two closely spaced frequencies (relative separation ∼0.2% to 2%, strongly dependent on tension.) The two frequency components are associated, respectively, with the transverse motion along two orthogonal characteristic wire axes. Emphasis will be on display of optically detected unusual motion patterns of a point on the string, including an example of a pattern period of 10 s when driving at 50 Hz. See R. J. Hanson et al., J. Acoust. Soc. Am. 117, 400–412 (2005) for a more complete treatment.