Measurements Of Nonlinear Effects In A Driven Vibrating-Wire

Experimental measurements have been made of the motion of a red brass harpsichord wire driven electromagnetically in a fixed direction perpendicular to the equilibrium position of the wire. The motion is complex compared to that predicted by simple linear theory because of effects due to tensional changes and longitudinal motions. Optoelectronic detectors are used to measure amplitude and phase of the transverse motions as functions of the driving frequency, both in the driving direction y and the direction z perpendicular to y. Near the free-vibration fundamental frequency f(0) the z and y amplitudes are comparable even for a very low driving force and amplitude. Amplitude jumps and hysteresis effects are observed for large amplitudes. The z-y phase difference is measured as 0 degrees, 90 degrees, and 180 degrees in different frequency regions, yielding both planar and whirling or tubular motion. As the driving frequency increases, the phase difference between the driving force and the y motion varies steadily from 0 degrees to 90 degrees before jumping to 180 degrees. There is no evidence of a critical frequency of onset of the z motion as is predicted in some theoretical treatments. Similar effects are observed near 3f(0), for which amplitude measurements have been made down to 0.01 mu m for a 0.71-m-long wire.