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The General Dispersion Relation for the Vibration Modes of Helical Springs

Author

Listed:
  • 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)

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.

Suggested Citation

  • Leopoldo Prieto & Alejandro Quesada & Ana María Gómez Amador & Vicente Díaz, 2022. "The General Dispersion Relation for the Vibration Modes of Helical Springs," Mathematics, MDPI, vol. 10(15), pages 1-18, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2698-:d:876164
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