SPATIAL MOTION OF A STRING SUBJECTED TO TWO HARMONIC EXCITATIONS WITH DIFFERENT FREQUENCIES

摘要

This paper studies spatial motion of a stretched string subjected to two harmonic excitations with different frequencies. Two cases are considered, one in which both excitations are in a plane, and one in which they are perpendicular to each other. First, theoretical analysis by the method of multiple time scales is conducted. It is found that in the former case sub-combination resonance and summed-and-differential combination resonance of whirling type can occur, and in the latter case sub-combination resonances parallel and perpendicular to the excitations and of whirling type can occur. Then, experiment is conducted. In the experiment, it was confirmed that the same types of motions as those predicted in the theoretical analysis occured. In addition, it was found that for the case in which the excitations are in a plane the response is sensitive to the difference between the natural frequencies in the two perpendicular directions. Finally, effect of the difference between the natural frequencies is studied.