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The influence of transported fluid on static and dynamic behaviors of marine risers is investigated. The internal flow of the transported fluid could have a constant, a linear, or a wave velocity. The riser pipe may possibly experience the conditions of high extensibility, flexibility, and large displacements. Accordingly, the mathematical riser models should be governed by the large strain formulations of extensible flexible pipes transporting fluid. Nonlinear hydrodynamic dampings due to ocean wave–pipe interactions implicate the high degree of nonlinearity in the riser vibrations, for which numerical solutions are determined by the state–space–finite-element method. It is revealed that the impulsive acceleration of internal flow could seriously relocate the vibrational equilibrium positions of the riser pipe. The fluctuation of the pulsatile flow relatively introduces the expansion of amplitudes and the reduction of frequencies of the riser vibrations. The pulsatile frequencies of the internal flow in wave aspect could reform the oscillation behavior of the conveyor pipe.

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This paper presents a large deflection of variable-arc-length beams, which are made from nonlinear elastic materials, subjected to its uniform self-weight. The stress-strain relation of materials obeys the Ludwick constitutive law. The governing equations of this problem, which are the nonlinear differential equations, are derived by considering the equilibrium of a differential beam element and geometric relations of a beam segment. The model formulation presented herein can be applied to several types of nonlinear elastica problems. With presence of geometric and material nonlinearities, the system of nonlinear differential equations becomes complicated. Consequently, the numerical method plays an important role in finding solutions of the presented problem. In this study, the shooting optimization technique is employed to compute the numerical solutions. From the results, it is found that there is a critical self-weight of the beam for each value of a material constantn. Two possible equilibrium configurations (i.e., stable and unstable configurations) can be found when the uniform self-weight is less than its critical value. The relationship between the material constantnand the critical self-weight of the beam is also presented.

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