It is known that, under certain conditions, a stretched string subjected to a planar harmonic excitation executes nonplanar motions due to the instability of the palanar motion. In recent years, studies on bifurcations of such nonplanar motions to amplitude modulated quasiperiodic motions and chaotic motions have been reported. However no literatures on the problem of nonplanar motions due to a multi-frequency excitation are found.
In this paper, the possibility of nonplanar motions in a string due to a two-frequency excitation is studied. For this purpose two cases are considered, i.e. one in which both components of the excitation are in a plane, and one in which they are perpendicular to each other. In both cases the sum of the frequencies of the components is supposed to near to twice one of the natural frequencies of the string. Theoretical analysis using the perturbation method of multiple scales and numerical simulation are carried out to show that nonplanar motions occur.