# Vibrating string theory

1. Jan 14, 2004

### yano

I am currnetly trying to model a coil winding process but I am not having much success as of yet. the process involves the winding of a platinum wire around a stainless steel mandrel and is at present experiencing vibration. there is constant tension on the mandrel and the mandrel is driven by two simultaniusly driven chucks (no torsional vibration). the point at which the platinum wire is being applied (to the mandrel) is changing its length from the chuck with respect to time as the wire is wound around the mandrel. when the prcess is finished the combined filament and mandrel combination resembles a guitar string, which lead me to the vibrating string formula. the vibration being experienced is transverse vibration. i have looked at the derivation of the vibrating string formula and have noticed that it was assumed that the displacement of the string and coresponding slopes were small and hence ignored. is it possible to derive a similar vibrating string formula taking into account the displacment caused by the tension of the platinum wire? once i have a suitable mathematical formula, would it be correct to differentiate this formula with respect to the length to account for the point of application of the platinum wire changing position with time. the objective would be to come up with a model of the process that could could predict where a mode of vibration will occur and then to change the rotational speed of the mandrel (which is the excitation frequency) so that a mode of vibration will occur outside of the system. i hope i have explained the problem as well as possible. thanking you in advance for any suggestions or replys, JP.