Prieto Fernández, LeopoldoQuesada González, AlejandroGómez Amador, Ana MaríaDíaz López, Vicente2023-03-102023-03-102022-08-01Prieto, L., Quesada, A., Gómez Amador, A. M., & Díaz, V. (2022). The General Dispersion Relation for the Vibration Modes of Helical Springs. Mathematics, 10(15), 2698.2227-7390https://hdl.handle.net/10016/36802This article belongs to the Special Issue Applied Mathematics to Mechanisms and Machines.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 ω = f (k) has been obtained to model a wave traveling along the axis of the wire.18eng© 2022 by the authors.Atribución 3.0 EspañaHelical springVibrationFrenet trihedralDispersion relationNatural frequencyresearch articleIngeniería IndustrialIngeniería MecánicaMaterialeshttps://doi.org/10.3390/math10152698open access115, 269818Mathematics10AR/0000032331