The General Dispersion Relation for the Vibration Modes of Helical Springs

Leopoldo Prieto, Alejandro Quesada, Ana María Gómez Amador and Vicente Díaz
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Leopoldo Prieto: Department of Mechanical Engineering, Universidad Carlos III de Madrid, 28911 Leganes, Spain
Alejandro Quesada: Department of Mechanical Engineering, Universidad Carlos III de Madrid, 28911 Leganes, Spain
Ana María Gómez Amador: Department of Mechanical Engineering, Universidad Carlos III de Madrid, 28911 Leganes, Spain
Vicente Díaz: Department of Mechanical Engineering, Universidad Carlos III de Madrid, 28911 Leganes, Spain

Mathematics, 2022, vol. 10, issue 15, 1-18

Abstract: 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.

Keywords: helical spring; vibration; Frenet trihedral; dispersion relation; natural frequency (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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