Dynamic analysis of a non-conservative band–wheel system with a moving boundary part 2: Numerical results

The dynamic formulations of a non-conservative band/wheel system with a moving boundary are derived in the companion paper by use of Hamilton’s principle and calculus of variation. In this paper, numerical simulations for the system are obtained in transient amplitudes of the string and positions of the moving boundary by a modified finite difference method (FDM). Since the moving boundary position may not locate exactly at a grid point for any computational time, a special technique of the FDM is proposed to approximate both the transversality condition of a moving boundary and the partial differential equation of the neighboring grid points. The effects of parameters such as radius of the wheel, tension of the string, propagation speeds of the longitudinal and transverse wave and various initial conditions on the transient responses are investigated and compared with those of the fixed boundary problem.