Claudio A. Rodríguez

On the Occurrence of Mathieu Instabilities of Vertical Cylinders

Large offshore platforms with vertical circular cylindrical hull shapes have been designed and employed in recent times. Classical spar platforms and mono-column concepts are just two examples of designs with such simple configuration, supposed to perform limited motion responses in waves. Reports on investigations on the occurrence of parametric resonance of spar platforms have been published recently in which the relevance of Mathieu amplifications have been assessed making use of different mathematical models. However, some uncertainties still remain on the influence of crucial design parameters as, for instance, metacentric height, draft/diameter ratio, associated damping and mooring system. In an attempt to clarify some of these aspects, in this paper the dynamic stability of a vertical cylinder in regular waves is investigated theoretically and experimentally. A coupled non-linear mathematical model is employed to model and simulate the coupled heave, roll and pitch motions. Theoretical aspects related to the development of resonant motions are discussed. In addition to the numerical and theoretical investigations, an extensive series of experiments with a model of a typical mono-column have been recently conducted at LabOceano. The findings of these investigations are compared and summarized.Copyright

Nonlinear Dynamics on Parametric Rolling of Ships in Head Seas

The present paper employs nonlinear dynamics tools in order to investigate the dynamical characteristics governing the complex coupling of the heave, roll and pitch modes in head seas at some regions of the numerical stability map of a fishing vessel. Bifurcation diagrams and Poincare mappings are computed and employed to investigate the appearance of multistability and chaos associated with increased values of the selected control parameter, the wave amplitude. The connection between these nonlinear characteristics and the coupled nature of the mathematical model are analyzed. Lyapunov exponents corresponding to the three coupled models are computed.

Nonlinear Instabilities of Spar Platforms in Waves

Spars are widely recognized as an excellent choice for deep water applications due to their hydrodynamic characteristics. However, some relatively recent works report the occurrence of large motions in the plane perpendicular to wave incidence direction, i.e., not directly excited by waves. These unstable motions have been attributed to Mathieu instabilities, caused by pure hydrostatic variations of the underwater hull geometry. Based on a new approach developed by the Authors for predicting parametric rolling in ships, this nonlinear phenomenon has been investigated for spar platforms. The proposed approach demonstrates analytical and numerically that unstable motions, in fact, may appear, but the mechanism that triggers parametric rolling is not related to variations in the hull hydrostatic characteristics. Nonlinear pressure variations induced by waves passing along the spar introduce parametric excitation. Different from typical ship forms, where this effect is negligible even in very long waves due to shorter draughts, in spars, this excitation can be significant, especially for very long waves. The present paper presents the analytical expressions for roll parametric excitation in spars and numerically explores the proposed approach applied to a typical spar under a wide range of wave heights and periods. Parametric Amplification Domains (PADs) were numerically computed, showing not only the boundaries of the instability regions but also the maximum roll amplitudes.Copyright

Domains of Parametric Roll Amplification for Different Hull Forms

A new 6-DOF nonlinear mathematical model based on Taylor-series expansions with coupling terms defined up to the third-order is introduced and validatedl for head seas parametric rolling for the case of a fishing vessel and a container vessel. Additionally, a large and deep drafted cylindrical SPAR platform is also simulated. The nonlinear algorithm is systematically simulated for different wave conditions. Parametric amplification domains (PADs) are thus obtained for the three hulls. On a comparative basis some of their main characteristics are then examined: influence of coupling, relevance of third-order coupling terms, impact of roll/roll nonlinearities, influence of wave amplitude, and initial conditions. The main differences in the PADs for the three distinct floating vessels are then interpreted and aspects of interest for the modeling and simulation of different hull forms are discussed.

An Experimental Approach for the Offshore Launching of Jack-Ups

Recently, as part of the building contract for the new Brazilian jack-up drilling platforms, an operational challenge was raised: to launch these units from the building site, where neither dry dock nor launching ground ways exist. Economically, the best alternative was to launch these jack-ups using the available barges used commonly for jacket launch. Due to the marked differences between a jacket and a jack-up, the implementation of this novel launch operation required a careful feasibility study. Model tests were required to measure the motions of the barge and the jack-up and to evaluate the loads on the barge rocker arms. The present paper discusses the experimental approach, test setup, calibration procedures, and some results from the hydrodynamics perspective.

A Nonlinear Numerical Algorithm for Time-Domain Hydrodynamic Simulations of Vessel Motions in the Presence of Waves

Linear approaches have been traditionally employed to simulate the dynamic behavior of floating vessels and its interaction with regular or irregular waves. Some difficulties arise when large waves and vessel motions occur. Under these circumstances, the linear assumptions to compute the restoring and wave forces, which are computed on the mean position of body and water surface, are not capable of accurately representing the physics of the interactions between waves and vessels.Hydrostatic analysis of generic hull forms has already been implemented with a geometrical face representation of the hull and also internal ballast and oil tanks [1]. With the goal of improving the modeling the non-linear computation of hydrostatic in waves (at the instantaneous free surface) is implemented, thus using a generic geometric modeling of the hull to perform hydrodynamic simulations of vessel motions in the presence of waves. Additionally, for the computation of the instantaneous non-linear Froude-Krylov force (6 DOF time-domain model) the contribution of each geometrical face to the global Froude-Krylov force is calculated at the exact relative position of the vessel and the incident waves. After computing the relative position of each face, possibly being cut at the free surface, the pressure at the wetted face centers determines the contribution to the integral calculation.The paper presents the main aspects of the proposed methodology and highlights its capabilities and differences with respect to the linear approach. Complementarily, comparisons with model experiments are discussed.Copyright

Experimental Assessment of the Offshore Launching Operation of a Jack-Up Unit

Recently, an experimental campaign was carried out to assess the feasibility of the launching operation of two jack-up units using a barge as the launching platform. This experimental study was divided in four stages. In stages 1 to 3, a series of preliminary model tests were performed in order to provide scientific understanding of the mechanics of the operation, and investigate systematically the influence of launching parameters. The experimental approach developed for testing this operation and the results of the preliminary launching tests have been discussed in detail in a previous paper [1]. Based on the analyses of the experimental results of stages 1 to 3 and, the results of numerical simulation tools, in stage 4, a final launching condition was designed and a new set of model tests were specified to check the safety of the operation. This paper presents the results and analyses of the experimental tests in stage 4. The conditions tested in this stage covered the expected real launching condition and possible deviations in some launch parameters. The tests results include the 6-DOF motions and trajectories of the launched jack-up and the launch barge, and the reaction forces on the barge rocker arms. Later on, the success of the launching operations of P-59 and P-60 jack-up units confirmed the experimental investigation results and the feasibility of this novel launching procedure. Furthermore, it can be concluded that the experimental approach efficiently served as a tool for the assessment of high risk operations.© 2014 ASME

Offshore Launching of Jack-Up Units: An Experimental Approach

Ships and most offshore structures are commonly launched into water from dry docks. But, sometimes due to practical and economical restrictions, launching of some offshore structures takes place at floating launching platforms, usually barges. The latter type of launching is quite “usual” for jacket rigs. To assess the success of the launch operation usually numerical simulations are enough and model tests are usually not required. However, more recently, as part of the construction project of the new Brazilian jack-up oil platforms, an innovative launching operation was required: launching a jack-up using a jacket launching barge. The marked differences between the two types of structures involve hydrodynamic and structural complexities. From the hydrodynamical point of view, due to its greater volume compared to jackets, the jack-up may be subjected to greater loads as enters in water during launching, and then suffers great motions that may affect the barge motions and these, affect back, the jack-up motions. From the structural point of view, the heavier jack-up structure may cause greater stresses on the barge deck and rocker arms that should be properly addressed in order to determine the necessity for reinforcements in the jack-up and/or the barge. To assess the feasibility of this innovative launching operation, model tests were required to measure the motions of the barge and the jack-up and to evaluate the loads on the rocker arms. The present paper describes the experimental approach developed for simulating this unique launching operation. The calibration procedures are outlined and the main results of the systematic set of tests carried out are presented. Furthermore, the influence of some launching parameters such as friction coefficient, position of the center of gravity of the jack-up and initial launching angle are discussed.Copyright

An Investigation on Head-Sea Parametric Rolling for Two Fishing Vessels

The paper describes an experimental and numerical investigation on the relevance of parametric resonance for two typical fishing vessels in head seas. The investigation is aimed at assessing the influence of the incorporation of a transom stern to the design. Results for different Froude numbers are discussed. The first region of resonance is investigated. Distinct metacentric heights and wave amplitudes are considered. Quite intense resonances are found to occur. These are associated with specific values of metacentric height, ship speed and stern shape. In order to analyse the experimental/numerical results, analytic consideration is given to distinct parameters affecting the dynamic process of roll amplification. The influences of heave, pitch, wave passage effect, speed and roll restoring characteristics are discussed.

Control of Unstable Ship Motions Using Anti-Rolling Tanks: Erosion of Safe Basins

The objective of the paper is to apply modern numerical techniques of nonlinear dynamics to the problem of control of the roll motion employing U-shaped anti rolling tanks (ART). Parametric rolling in head seas is the focus of the paper. A transom stern small vessel, well known for her tendency to develop strong parametric excitation is investigated. Nonlinear equations are employed to describe the liquid motion inside the tank, the forces and moments generated by the tank on the ship and the coupled ship motions (heave, roll and pitch). These are numerically solved for different initial conditions. An analysis of the dynamical behavior of the vessel with stabilization is presented in the form of numerical limits of stability, safe basins, integrity curves and integrity surfaces. Finally, curves of critical amplitude for different wave tunings are computed. A design procedure for quantitative assessment of the level of parametric rolling mitigation by means of ART’s is discussed.Copyright