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The General Dispersion Relation for the Vibration Modes of Helical Springs

A system of mathematical equations was developed for the calculation of the natural frequencies of helical springs, its predictions being compared with finite element simulation with ANSYS®. Authors derive the general equations governing the helical spring vibration relative to the Frenet trihedral representing the normal, binormal and tangent unit vectors to the spring medium line. The dispersion relation has been obtained to model a wave traveling along the axis of the wire.