In-Plane Free Oscillations of Suspended Chains
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Abstract
Chain dynamics are of particular interest in high-voltage power lines, as chain drives in cars’ motors, motorcycles, maritime anchoring of ships, and even some bridge suspensions. The equilibrium and linear oscillations of a heavy, homogeneous chain made of identical rigid links, suspended between two fixed points at different heights, are investigated. The problem of the equilibrium position of each link is solved using an original algorithm based on Lagrange multipliers, being followed by some relevant numerical examples. The chain is in a gravitational field, and the kinetic energy and force function are deduced as an original compact formula, valid for any number of links. We obtained the Lagrange equations with motion constraints imposed by the fixed positions of the two ends of the chain. The free oscillations in the vertical plane passing through the hanging points are deduced, and several numerical examples are presented.
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