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Applied Mechanics, Behavior of Materials, and Engineering Systems pp 227–238Cite as

Natural Frequencies of Composite Cylindrical Helical Springs

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Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Abstract

This study presents a method for calculating the natural frequencies of a Carbon-Epoxy helical spring. The mathematical formulation presented describes the linear dynamic behavior of composite excited helical springs. The governing mathematical model of such behavior is formed by a system of four partial differential equations of first order of hyperbolic type. This system describes the axial and rotational wave propagation of strains and velocities, which are the primary dependent variables. They depend on time and the space coordinate along the spring axis. These waves propagate in the spring with two speeds; the speed of slow axial waves and the speed of the fast rotational waves. To simplify mathematical model, the spring is assumed to be homogeneous. The mechanical and geometrical characteristics of the spring are obtained by a weighted average of those of its two components. The area fraction is used as weights. The impedance method is then applied to determine the natural frequencies of the spring. The results show the existence of two sets of resonance frequencies, the frequencies of slow axial waves and those of rapid rotational waves. They correspond to the fundamental and odd harmonics of the system. Each resonant frequency is separated in the impedance diagram by an anti-resonance frequency, the impedance at which the module is zero. The results clearly show the influence of the area fraction on the evolution of the natural frequencies of composite helical springs.

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Author information

Authors and Affiliations

  1. Laboratory of Applied Fluid Mechanics, Process Engineering and Environment, ENIS, BP 1173, 3038, Sfax, Tunisia

    Sami Ayadi & Ezzeddine Haj Taïeb

Authors
  1. Sami Ayadi
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  2. Ezzeddine Haj Taïeb
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Corresponding author

Correspondence to Sami Ayadi .

Editor information

Editors and Affiliations

  1. Lab for Advanced Mechanics, USTHB, Bab-Ezzouar, Algeria

    Taoufik Boukharouba

  2. Metz, France

    Guy Pluvinage

  3. Laboratoire de Mécanique Avancée (LMA), (USTHB), Bab-Ezzouar, Algeria

    Krimo Azouaoui

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Ayadi, S., Haj Taïeb, E. (2017). Natural Frequencies of Composite Cylindrical Helical Springs. In: Boukharouba, T., Pluvinage, G., Azouaoui, K. (eds) Applied Mechanics, Behavior of Materials, and Engineering Systems. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-41468-3_18

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  • DOI: https://doi.org/10.1007/978-3-319-41468-3_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-41467-6

  • Online ISBN: 978-3-319-41468-3

  • eBook Packages: EngineeringEngineering (R0)

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