Dynamics of Geometrically Linear and Nonlinear Cable Structures Subject to Moving Mass

In this work, we derive the governing equation using Hamilton’s principle for a system modeled as a linear classical string subjected to a moving mass. This mass has rotary inertia, and its motion is defined relative to the string. We then consider two initial-boundary value problems (IBVPs) for the string with respect to the moving mass: (i) a stretched string and (ii) a hanging string. For both systems, we analyze the well-known trajectory paradox associated with the stretched string and the phenomenon of sudden large rotation of the moving mass at the free end of the hanging string. We also outline the limitations and drawbacks of using the linear model for these systems. To address these limitations, we examine a geometrically exact rod model subjected to a moving mass, exploring both cases. This model demonstrates that there is no occurrence of the trajectory paradox or sudden significant rotation in these IBVPs.