Vibration suppression of a string through cyclic application and removal of constraints

A new method for the control of string vibration is presented. The method relies on application and removal of a constraint at one point on the string close to one of its boundaries. Application of the constraint temporarily results in two vibrating strings, one of which is significantly shorter in length than the other. The vibration of the shorter length string decays rapidly due to high damping and results in reduction in the overall energy of the system. Removal of the constraint does not change the energy of the system but allows the constraint to be applied repeatedly for vibration suppression. A mathematical model of the cycle of constraint application and removal is presented and multiple cycles of constraint application and removal are simulated. Experiments were performed with a coiled extension spring which behaves like a lightly damped string. Simulation and experimental results match well with each other and demonstrate the efficacy of the simple control strategy.