SUPPRESSION OF STRING VIBRATION USING A CONSTRAINT ACTUATOR AT ONE BOUNDARY

摘要

The problem of a vibrating string subjected to a sudden constraint at one boundary is investigated in this paper. The constraint is imposed by a sleeve that axially moves along the mean position of the string with a small distance. The constraint is applied instantaneously such that the geometry of the string outside the sleeve, immediately after application of the constraint, remains unchanged whereas the length of string covered by the sleeve remains at rest. The change in energy of the string after application and removal of the sleeve is investigated for different values of sleeve travel distance and time of application of the constraint. Analytical and numerical simulation results are first provided for the string vibrating in the first mode, and then for a more general case where the string has arbitrary initial conditions. The results show that the energy content can decrease or increase depending on the time of application of the constraint and sleeve travel distance. This provides the opportunity for active control of string vibration through direct physical interaction with a small portion of the string by using the sleeve as an actuator.