Parametric Resonances of Columns

  • Yoshihiko SugiyamaEmail author
  • Mikael A. Langthjem
  • Kazuo Katayama
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 255)


This chapter aims to give a general overview of the parametric resonances of columns under a harmonically pulsating force. In addition to simple resonance, combination resonances of sum and difference type are introduced, with columns having various kinds of boundary condition, other than pinned-pinned ends. For simplicity, it is assumed that damping is absent. Hsu’s conditions for resonances are introduced to give the first estimate of the principal regions of instability. Experiments with columns having clamped-clamped and clamped-pinned ends are presented, to demonstrate combination resonances of sum type. Combination resonances of difference type are introduced through an analog computer-based experiment of a cantilevered column subjected to a pulsating follower force.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Yoshihiko Sugiyama
    • 1
    Email author
  • Mikael A. Langthjem
    • 2
  • Kazuo Katayama
    • 3
  1. 1.Small Spacecraft Systems Research CenterOsaka Prefecture UniversitySakaiJapan
  2. 2.Department of Mechanical Systems EngineeringYamagata UniversityYonezawaJapan
  3. 3.Daicel CorporationTatsunoJapan

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