Transient and Steady-State Response of Constrained Translating Strings

The exact expression describing the constraint force in a constrained translating string is derived using the Green’s function formulation. Discontinuity of the initial velocity at a boundary of the string due to a disturbance causes discontinuity in the constraint force history for any constraint that is not modeled by a single spring element. The discontinuities in the constraint force occur at instants when those propagating wave-fronts in the string with non-vanishing slope interact with the constraint. A model of a magnetic tape-recording head system is analyzed. Tape-head contact loss is predicted, depending on the amplitude and frequency of the disturbance, the head location and the preload of the tape against the head. The transient response to a harmonic end excitation is compared at the steady state to the closed-form prediction of a steady forced analysis.