Planar non-linear free vibrations of an elastic cable

Angelo Luongo (1) , Giuseppe Rega (2) , Fabrizio Vestroni (2)

1 DICEAA - Dipartimento di Ingegneria Civile, Edile-Architettura, Ambientale
2 DISG - Dipartimento di Ingegneria Strutturale e Geotecnica

Continuum non-linear equations of free motion of a heavy elastic cable about a deformed initial configuration are developed. Referring to an assumed mode technique one ordinary equation for the cable planar motion is obtained via a Galerkin procedure, an approximate solution of which is pursued through a perturbation method. Suitable nondimensional results are presented for the vibrations in the first symmetric mode with different values of the cable properties. Which procedure is the proper one to account consistently for the non-linear kinematical relations of the cable in one ordinary equation of motion is discussed.

Domaines: Génie civil

Angelo Luongo, Giuseppe Rega, Fabrizio Vestroni. Planar non-linear free vibrations of an elastic cable. International Journal of Non-Linear Mechanics, 1984, 19 (1), pp.39-52. ⟨hal-00787648⟩