Abstract:
The transverse vibration of an axially accelerating string is investigated. The equation of motion is developed using Hamilton's principle. The resulting partial differential equations are discretized using Galerkin's method. Retaining one-term in Galerkin's approximation leads to a Mathieu equation, the solution of which is well known. In the two-term approximation the resulting coupled equations are solved by numerical methods. Results of the one-term and two-term approximations are compared, and it is concluded that the one-term approximation is not adequate for capturing the basic transverse instability mechanisms of the axially accelerating string.
