FREE ANDFORCED VIBRATIONOF ANAXIALLYMOVING STRINGWITHANARBITRARYVELOCITYPROFILE

摘要

The exact response of an axially moving stringwith an arbitrary velocity profile is determined undergeneral initial conditions and external excitation. Interms of the curvilinear characteristic coordinates thetime-dependent governing equation reduces to one withconstant coefficients. The domain of interest in thecharacteristic coordinate plane is bounded by two monotoniccurves with the same shape corresponding to thespatial boundaries of the string. Solution of thetransformed equation is derived for the free and forcedresponses. The displacement of the free response isshown to be bounded under arbitrary variation of thetransport speed in the subcritical regime. Parametricresonances do not exist. The method is demonstrated ontwo illustrative examples with piecewise constant andsinusoidal accelerations.