Equations of motion of a thin, stranded elastic cable with an eccentric, attached mass and subject to aerodynamic loading are derived using Hamilton’s principle. Coupling between the translational and rotational degrees of freedom owing to inertia, elasticity, and stranded geometry are considered. By invoking simplifying assumptions, the equations of motion are reduced to those obtained previously by other researchers.
The Equations of Motion for the Torsional and Bending Vibrations of a Stranded Cable
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White, W. N., Venkatasubramanian, S., Lynch, P. M., and Huang, C. D. (June 1, 1992). "The Equations of Motion for the Torsional and Bending Vibrations of a Stranded Cable." ASME. J. Appl. Mech. June 1992; 59(2S): S224–S229. https://doi.org/10.1115/1.2899493
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