Nonlinear effects in an asymmetrical vibrating wire

Abstract

The asymmetries of a vibrating harpsichord wire which yield different free vibrational frequencies along two characteristic orthogonal transverse axes were described previously [Hanson et al., J. Acoust Soc. Am. 106, 2141 (1999)]. This splitting of the fundamental vibrational frequency is of the order of 0.3%. Its value depends upon the particular wire sample and the tension, with lower tensions yielding larger absolute splittings. For the 2nd, 3rd and 4th vibrational modes, splittings differ greatly from integral multiples of the splitting of the fundamental. If the wire is driven sinusoidally there can be large nonlinear generation of motion in a direction (P) perpendicular to the driving direction (D) and of higher harmonics of the driving frequency. These nonlinear effects are, however, very sensitive to the frequency splitting and the relation of the driving direction to the characteristic axes. Theory indicates that P/D∼1, independent of the vibrational amplitude. However, with a small splitting of 0.11 Hz out of 77 Hz, it was found that to obtain P/D∼1 an amplitude at the antinode of about 0.15% of the wire length was necessary. The driving frequency region for generation of higher harmonics is sharply dependent on the higher free-vibration mode frequencies.