Natural frequencies and mode shapes of statically deformed inclined risers. (September 2017)

• Record Type: Journal Article
• Authors: Alfosail, Feras K.; Nayfeh, Ali H.; Younis, Mohammad I.
• Is Part Of: International journal of non-linear mechanics. Volume 94(2017)
• Page Start: 12
• Page End: 19
• Publication Date: 2017-09
• Subjects: Inclined riser -- Natural frequency -- Mode shapes -- Galerkin method; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2016.09.007
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: We investigate numerically the linear vibrations of inclined risers using the Galerkin approach. The riser is modeled as an Euler–Bernoulli beam accounting for the nonlinear mid-plane stretching and self-weight. After solving for the initial deflection of the riser due to self-weight, we use a Galerkin expansion employing 15 axially loaded beam mode shapes to solve the eigenvalue problem of the riser around the static equilibrium configuration. This yields the riser natural frequencies and corresponding exact mode shapes for various values of inclination angles and tension. The obtained results are validated against a boundary-layer analytical solution and are found to be in good agreement. This constitutes a basis to study the nonlinear forced vibrations of inclined risers. Highlights: Investigate the linear vibrations of inclined risers using the beam mode shapes in Galerkin approach. The riser model accounts for the nonlinear mid-plane stretching, self-weight and static deflection. Demonstrate the structural softening behavior which affected the natural frequency values at higher configuration angles. Study the effect of applied tension and internal velocity shows internal resonances that can lead to complex dynamics.