Natural frequencies and mode shapes of statically deformed inclined risers

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 midplane stretching and self-weight. After solving for the initial deflection of the riser due to selfweight, 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.

Three-to-one internal resonance of inclined marine riser

“…The mode shapes and the natural frequencies of the structure are extracted by solving Eq. (8), using unforced beam mode shapes, via the Galerkin method [21]. For the analysis of the forced vibration part, one needs to consider the forces induced by vortex induced vibrations because they are the most detrimental to the riser structure.…”

“…In an earlier study [21], we have demonstrated that tuning the offset and the applied top tension introduce potentially several internal resonances among the various vibration modes, such as two-to-one, three-to-one, and four-to-one. Due to the lack of extensive research on this subject, the aim of this paper is to investigate the three-to-one internal resonance of the riser accounting for the static deflection and mid-plane stretching while the riser is subjected to harmonic excitation.…”

A state space approach for the eigenvalue problem of marine risers

“…We note that the presented state-space method is not applicable for solving marine riser systems with static deflection [35,36]. The deflection introduces a non-homogenous linear term from the geometric nonlinearity in which the numerical state of the end condition becomes nonzero.…”

On the delicate state of instability of a vertical riser transporting fluid

“…Additionally, we will show how the modal analysis for the vertical riser and the catenary-type riser can also be dramatically different. To provide this explanation, we found that we needed to extend and complement earlier works such as Klaycham et al (2017) and Alfosail et al (2017) by considering both in-plane and out-of-plane modes and fluid transport.…”