Dynamic analysis of a non-conservative band-wheel system with a moving boundary Part 1: Mathematical modelling

The dynamic band/wheel system with a moving boundary is very different from that with a fixed length, it is a non-conservative mass system and the boundary position is not fixed. In this paper, the moving boundary is one unknown to be determined associated with the string displacement, and the partial differential equation of the transverse vibrations of the band and the transversality condition of the moving boundary are derived by the calculus of variation and Hamilton’s principle. In order to verify the dynamic formulation is correct, we reduce the governing equation and separation point to coincide with the previous studies. It is found that the physical properties of the moving boundary could be obtained from the geometric constraint of the band/wheel system.