An analytic solution of the static problem of inclined risers conveying fluid

Alfosail, Feras K.; Nayfeh, Ali H.; Younis, Mohammad I.

doi:10.1007/s11012-016-0459-2

Cited by 12 publications

(7 citation statements)

References 23 publications

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“…The riser static profiles shown infigure 2are obtained for a large value of the nonlinear mid-plane stretching for various inclination angles and tensions. In all of the configurations, a good agreement is obtained between the perturbation solution[25] and the five-mode Galerkin approximation.…”

mentioning

confidence: 58%

“…We solve equation (2) using the method of matched asymptotic expansions [11] with clampedclamped boundary conditions [25]. The static solution is exact and complete.…”

Section: Problem Formulationmentioning

confidence: 99%

“…[25] to validate the proposed Galerkin approximation utilizing five basis functions. The riser static profiles shown infigure 2are obtained for a large value of the nonlinear mid-plane stretching for various inclination angles and tensions.…”

mentioning

confidence: 99%

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Natural frequencies and mode shapes of statically deformed inclined risers

Alfosail

Nayfeh

Younis

2017

International Journal of Non-Linear Mechanics

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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.

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mentioning

confidence: 58%

“…We solve equation (2) using the method of matched asymptotic expansions [11] with clampedclamped boundary conditions [25]. The static solution is exact and complete.…”

Section: Problem Formulationmentioning

confidence: 99%

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Natural frequencies and mode shapes of statically deformed inclined risers

Alfosail

Nayfeh

Younis

2017

International Journal of Non-Linear Mechanics

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“…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.…”

Section: Parametric Investigationmentioning

confidence: 96%

A state space approach for the eigenvalue problem of marine risers

2017

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A numerical state-space approach is proposed to examine the natural frequencies and critical buckling limits of marine risers. A large axial tension in the riser model causes numerical limitations. These limitations are overcome by using the modified Gram-Schmidt orthonormalization process as an intermediate step during the numerical integration process with the fourth-order Runge-Kutta scheme. The obtained results are validated against those obtained with other numerical methods, such as the finite-element, Galerkin, and power-series methods, and are found to be in good agreement. The state-space approach is shown to be computationally more efficient than the other methods. Also, we investigate the effect of a high applied tension, a high apparent weight, and higher-order modes on the accuracy of the numerical scheme. We demonstrate that, by applying the orthonormalization process, the stability and convergence of the approach are significantly improved.

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“…The static equation is solved using the method of matched asymptotic expansion [32]. Then, the dynamic equation of the inclined riser around equilibrium is obtained by substituting Eq.…”

Section: Problem Formulationmentioning

confidence: 99%

Multifrequency excitation of an inclined marine riser under internal resonances

Alfosail

Younis

2019

Nonlinear Dyn

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We study the multifrequency excitation of an inclined marine riser under two-to-one and three-toone internal resonances. The riser model accounts for the initial static deflection, self-weight, and mid-plane stretching nonlinearity. By tuning the initial applied tension and configuration angles of the riser, the ratio between its first and third natural frequencies approaches two. In another case, the ratio between its first and fifth natural frequencies approaches three. As recently revealed by experimental observations, a riser can experience multifrequency vortex-induced vibrations. Hence here, the excitation frequencies are tuned such that one frequency is near the first primary resonance while the other frequency is near the second primary resonance. The multiple time scales perturbation method is used to analyze the nonlinear motion of the riser considering the internal resonances. Frequency response results of the perturbation method are compared to a Galerkin solution, which show good agreement. The perturbation results in the two-to-one internal resonance case demonstrate that increasing the forcing amplitude at the second primary resonance suppresses the energy exchange due to internal resonance and reduces the likelihood of Hopf bifurcations while an opposite trend is observed in the three-to-one internal resonance case. Then, the dynamic solutions of the modulation equations of the perturbation method are analyzed using the Floquet theory to examine the post-Hopf bifurcation response. The limit cycle responses in both internal resonance cases exhibit several period doubling bifurcations possibly leading to quasi-periodic and other complex motions, which can endanger the life of the riser.

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An analytic solution of the static problem of inclined risers conveying fluid

Cited by 12 publications

References 23 publications

Natural frequencies and mode shapes of statically deformed inclined risers

Natural frequencies and mode shapes of statically deformed inclined risers

A state space approach for the eigenvalue problem of marine risers

Multifrequency excitation of an inclined marine riser under internal resonances

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