Transverse Modal Vibrations of Vertical Tensioned Risers. a Simplified Analytical Approach

Abstract

Résumé -Vibrations transverses modales de risers verticaux tendus. Approche analytique simplifiée -Le présent article est consacré à l'analyse structurelle des vibrations transverses modales d'un riser vertical tendu. Ces vibrations, souvent de type VIV (Vortex Induced Vibrations), apparaissent en présence d'un courant lorsque la fréquence des lâchers tourbillonnaires coïncide avec une des fréquences propres de la structure. Une approche analytique simplifiée est proposée pour le cas d'un riser possédant des caractéristiques de poids apparent et de masse linéique uniformes. Des formules très simples sont ainsi obtenues pour les paramètres structurels les plus significatifs : fréquences propres, positions des noeuds et des ventres, débattements angulaires en tête et en pied, valeurs et positions des points de courbure maximale. Les formules obtenues permettent de mieux comprendre la réponse structurelle d'un riser en eau profonde en condition dite « d'accrochage », pour le phénomène de VIV.

Natural vibration analysis of tensioned risers by segmentation method

“…By following Sparks (2002), (4) where according to (2), (6) and (7): (9) The solution of (8) yields: (10) where J 0 (z) and Y 0 (z) are Bessel functions of the first and second kind of order zero (Kreyszig, 1993;Abramowitz and Stegun, 1968). The relative value of the integration constants A and B, and natural frequency ω n contained in the argument of Bessel functions (9) depend on the given boundary conditions.…”

“…The equivalent forces are related to the vibration antinodes (Sparks, 2002). According to (19) for the mode adjacent nodes yields: (43) By substituting (23) into (42) one finds:…”

“…Thus, a suggestion concerning this matter, given in Sparks (2002), leads to a rather rough approximate solution especially for higher modes. Therefore, the problem is solved in a more reliable way by the so-called segmentation method, following the idea presented in Sparks, 2002.…”

“…Therefore, in order to simplify the procedure the riser vibration analysis is usually based on cable vibration theory and its analogical extension to the beam vibration problems. Thus, a rather simplified analytical approach is described in Sparks (2002) in order to explain the physics of riser dynamics. However, it is possible to solve the problem by the same approach but in a more sophisticated way.…”

“…In order to analyse the beam vibration, the cable solution is modified following an idea elaborated in Sparks (2002). However, the procedure is formulated in a somewhat different way.…”