COUPLING BETWEEN MODES OF THE ASYMMETRICALLY-FORCED STRETCHED STRING

摘要

A stretched string that is harmonically forced in oneplane may exhibit motion in a perpendicular plane. Previousstudies (see Bajaj and Johnson (1992)) have shownthat if only one mode is directly excited in the plane ofthe excitation, the steady-state motion in the perpendicularplane will contain large amplitude motion only in thesame mode. In other words, large amplitude, non-planaroscillations may occur only for n:n (e.g., 1:l or 2:2) coupling.In this paper, it is shown that this result is not truefor situations in which the mean force applied to the stringis non-zero. A bias force, in combination with harmonicexcitation at the second resonant frequency leads to outof-plane motion of the first mode of the string. This 2:lresonance is predicted by first-order averaging and is alsoseen in simulations and experiments.