The nonlinear free vibration of a damped elastic string
Colin E Gough · The Journal of the Acoustical Society of America · 1984
A theoretical analysis of the large-amplitude free vibration of a damped elastic string shows that the perturbation in vibrational frequency and the precession of any orbital motion of the string about its equilibrium position resulting from nonlinearity is simply related to the mean-square radius and area of the orbital motion. A computer simulation of the coupled nonlinear equations of motion and measurements made on a loosely stretched string confirm our theoretical predictions, which differ from those of an earlier analysis by Anand [J. Acoust. Soc. Am. 45, 1089–1096 (1969)]. The significance of nonlinear string vibration is considered for musical instruments.