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In oil and gas installations, whether on-shore or off-shore, pipes are the primary vessel for the conveyance of either crude or products from one location to another. Under use, the pipes are subjected to both internal and external temperature fluctuations while repeated operational start-up and shut-down procedures triggers vibrations of these pipes, propagates internal waves and results in finite and irreversible longitudinal extension of the pipe over time. This longitudinal extension which is sometimes accompanied by pipe buckling is known as ratcheting and has also been described by some as pipe walking. In view of the complicated and intractable nature of the problem, most attempts to study the behavior of these pipes have been limited to the analysis of some reduced problem based on heuristic arguments and idealizations. Within this context, the transverse vibration and stability of such pipes have been studied while the problem of undamped clamped-pinned pipe conveying fluid has also been tackled numerically. Keiper and Metrikine [2004] however pointed out that such numerical schemes sometimes lead to disputed or controversial results. More importantly, the coupling between the transverse vibration and longitudinal motion has been largely ignored or neglected altogether by most writers. The objective of this paper is to formally derive the governing equations of Euler-Bernoulli beam capturing various effects including temperature variations (within and without), Coriolis acceleration, transverse acceleration, pre-stress, pressurization, rotatory inertia, and cross-sectional area change. In particular, it is shown that the latter effect is what causes pipe walking phenomenon. Most of the other effects were either earlier accounted for by Semler, et al [1994] or recently captured by Reddy and Wang [2004]. Nonetheless earlier contributions neglected the effect of the cross-sectional area change completely, thereby omitting the pipe walking phenomenon. Simple examples are considered to demonstrate the importance of these terms.

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The dynamic response interaction of a vibrating offshore pipeline on a moving seabed is herein investigated where the pipeline is idealized as a beam vibrating on an elastic foundation. In particular the time history effects on physics of the stress distributions on the dynamic interaction predicted on sea state and waves is studied. The spectral density analysis of responses and stress distributions over time is used to predict the anticipated time for pipe burst using the seabed state. The studies also revealed that in general, the seabed acts either as a damper or as a spring and in particular when we have sedimentation, the seabed geology permits the geo-mechanical property of the sediment cover to act only as a damper. As expected, external excitation will increase the response of these pipes for which an amplification factor has been derived. For soft beds, high transverse vibrations were dampened by increasing the internal fluid velocity whereas they became amplified for hard beds.

This paper studied the nonlinear vibrations of top-tensioned cantilevered pipes conveying pressurized steady two-phase flow under thermal loading. The coupled axial and transverse governing partial differential equations of motion of the system were derived based on Hamilton's mechanics, with the centerline assumed to be extensible. Using the multiple-scale perturbation technique, natural frequencies, mode shapes, and first order approximate solutions of the steady-state response of the pipes were obtained. The multiple-scale assessment reveals that at some frequencies the system is uncoupled, while at some frequencies a 1:2 coupling exists between the axial and the transverse frequencies of the pipe. Nonlinear frequencies versus the amplitude displacement of the cantilever pipe, conveying two-phase flow at super-critical mixture velocity for the uncoupled scenario, exhibit a nonlinear hardening behavior; an increment in the void fractions of the two-phase flow results in a reduction in the pipe's transverse vibration frequencies and the coupled amplitude of the system. However, increases in the temperature difference, pressure, and the presence of top tension were observed to increase the pipe's transverse vibration frequencies without a significant change in the coupled amplitude of the system.

In aerodynamic and machine structures, one of the effective ways of dissipating unwanted vibration or noise is to exploit the occurrence of slip at the interface of structural laminates where such members are held together in a pressurised environment. The analysis and experimental investigation of such laminates have established that when subjected to either static or dynamic loading, non-uniformity in interface pressure can have significant effect on both the energy dissipation and the logarithmic damping decrement associated with the mechanism of slip damping. Such behaviour can in fact be effectively exploited to increase the level of damping available in such a mechanism. What has however not been examined is to what extent is the energy dissipation affected by the relative sizes or the material properties of the upper and lower laminates? In this paper the analysis is extended to incorporate such effects. In particular, by invoking operational methods, it is shown that variation in laminate thickness may provide less efficacious means of maximizing energy dissipation than varying the choice of laminate materials but that either of these effects can in fact dwarf those associated with non-uniformity in interface pressure. To achieve this, a special configuration is required for the relative sizes and layering of the laminates. In particular, it is shown that for the case of two laminates, the upper laminate is required to be thinner and harder than the lower one. These results provide a basis for the design of such structures.

In the course of operation of pipes conveying high temperature-high pressure fluid, unexpected behaviors leading to catastrophic failures have been observed. These have been attributed to uncertainties arising from issues not adequately addressed in the design. Sources of such uncertainties include geometric imperfection of the pipe and temperature variation. The perfectly straight pipe is assumed in most designs, but it is an idealization that does not exist in practice. In a bid to reduce the number of uncertainties in design and operation, a model governing nonlinear vibration of tensioned pipes conveying hot pressurized fluid that accounts for the geometric imperfection of the pipe is developed in this work. Coupled nonlinear equations of motion in both axial and transverse directions are obtained and solved using the eigenfunction expansion method. The influence of initial curvature, temperature, and the longitudinal vibration on the pipe are investigated. The results obtained show that a pipe with geometric imperfection exhibits cusp bifurcation and not supercritical pitchfork bifurcation.