Ioannis K. Chatjigeorgiou

Bounded and unbounded coupled transverse response of parametrically excited vertical marine risers and tensioned cable legs for marine applications

The paper deals with the non-linear dynamic response in the transverse direction of vertical marine risers or a tensioned cable legs subjected to parametric excitation at the top of the structure. The dynamic model contains both elastic and bending effects. The analytical approach reveals that the dynamic lateral response is governed by effects originated from the coupling of modes in transverse direction. The mathematical model is being treated numerically by retaining a sufficient number of transverse modes. Numerical results are given for specific case studies and refer both to the time histories of the lateral response for all modes of motion, and to the corresponding power spectral densities obtained through FFT. The numerical predictions are suitably plotted and discussed. The calculations concern both the undamped and the damped dynamic system. The damping in the system is a non-linear Morison type term, which describes the effect of the hydrodynamic drag. Both coupled and uncoupled equations are treated and points as well as regions of coupled and uncoupled stability and instability are defined. It is shown that the impacts originated from the coupling, evaluate new instabilities for the respective undamped system. The numerical results obtained through FFT of the time histories, provide qualitative conclusions for the features of the dynamic response for the modes of motions considered. Special attention has been paid to the effect of the hydrodynamic drag for the parametric excitation frequencies that guide the dynamic system to lie within a region of coupled instability.

Numerical simulation of the chaotic lateral vibrations of long rotating beams

The purpose of the present study is to investigate the global nonlinear dynamic behavior of long circular beams spinning about their longitudinal axes. Special attention is given to the stimulation of chaotic regimes. Contrary to the usual formulations which apply a fortiori energy methods, the dynamic equilibrium system is obtained using a Newtonian derivation procedure. The final mathematical model that governs the three dimensional nonlinear dynamics of the rotating beam is further elaborated in the time domain by employing a combination of finite difference solvers that rely on the second-order accurate Keller Box and Crank-Nicolson schemes. Several numerical tests have been performed assuming a drillstring structural model. The calculations show that the evolutions of the dynamic components that govern the kinematics of the concerned mechanical system are indeed chaotic. That feature was demonstrated in several different ways and in particular through Lyapunov exponents, phase space Poincare maps and Power Spectral Densities of the time dependent variables.

Application of the WKB method to catenary-shaped slender structures

The purpose of this work is the derivation of closed form expressions for the linear vibration modes of catenary-shaped slender structures. The dynamic behaviour of the structure is described using the Euler-Bernoulli beam formulation with variable tension and angle terms. The desired expressions are obtained by treating the governing fourth-order partial differential equation of dynamic equilibrium using the WKB method [J.D. Logan, Applied Mathematics, second ed., Wiley Interscience, 1997].

Extreme Bending Moments on Long Catenary Risers Due to Heave Excitation

This paper deals with the dynamic behaviour of catenary shaped risers under imposed motions applied at the top. Particular attention is paid to the heave component of motion which is of substantial importance for practical applications as it results to the amplification of large bending moments in the touch down region. In fact, the bending moment obtains its maximum value at the vicinity of the touch down point and very close to the location of its maximum static counterpart. This singular behaviour is discussed using the results from the solution of the eigenvalue problem. To this end the eigenfrequencies and the corresponding mode shapes are calculated using the WKB approximation making no assumption regarding the variation of the static components. In addition, the feature of the correlation between the axial component of the velocity of the excitation and the extreme bending moments at the lower part (Passano and Larsen, 2006) is further investigated through comparative numerical calculations of the problem using both frequency and time domain techniques.Copyright

Wave Scattering of Spheroidal Bodies Below a Free Surface

A new multipole expansion method based on Havelock’s theorem is proposed for solving the hydrodynamic problem of a submerged spheroidmoving below a (linearized) free surface. In particular, the Green’s function thus derived can be used to determine the forces and moments exerted on an oscillating spheroid with forward motion (radiation and wave resistance) or a fixed spheroid in the presence of a monochromatic time-harmonic incident wave (diffraction). The authors present a solution for the diffraction problem, including some numerical simulations for the heave, sway, and surge forces as well as yawmoments acting on a prolate rigid spheroid (depending on its eccentricity) in the case of an oblique incident wave field.

Dynamics of shell-like tubular segments at the sagbend region of a steel catenary riser

Nonlinear finite element method (FEM) analyses are performed for the simulation of the dynamic stress conditions of tubular segments of a long catenary pipeline, corresponding to a particular steel catenary riser. The tubular segments are discretised with eight-node planar shell-elements. The transient analysis of each segment is accomplished via an implicit time integration scheme. The time-dependent loads and boundary conditions on each segment are primarily derived by the solution of an integrated line dynamics model that relies on a finite differences scheme. The present FEM solution aims at a more detailed depicture of the distribution of dynamic stresses, considering the pipeline as a shell structure instead of using the simplistic “line-dynamics” approach.

The 3D Nonlinear Dynamics of Catenary Slender Structures for Marine Applications

Riser systems are inextricable parts of integrated floating production and offloading systems as they are used to convey oil from the seafloor to the offshore unit. Risers are installed vertically or they are laid obtaining a catenary configuration. From the theoretical point of view they can be formulated as slender structures obeying to the principles of the Euler-Bernoulli beams. Riser-type catenary slender structures and especially Steel Catenary Risers (SCRs) attract the attention of industry for many years as they are very promising for deep water applications. According to the Committee V.5 of the International Ship and Offshore Structures Congress (ISSC, 2003), “flexible risers have been qualified to 1500m and are expected to be installed in depths up to 3000m in the next few years”. In such huge depths where the suspended length of the catenary will unavoidably count several kilometers, the equivalent elastic stiffness of the structure will be quite low enabling large displacements. The later remark implies that even small excitations could cause significant excursions in both in-plane and out-of-plane directions. Therefore a 2D formulation, although adequate in predicting the associated dynamics in the reference plane of the static equilibrium, it would be certainly a short approximation. Furthermore, in deep water installations, for practical reasons mainly, the riser should be configured nearly as a vertical structure in order to avoid suspending more material. The nearly vertical configuration which ends in a sharp increase of the curvature close to the bottom, results in extreme bending moments at the touch down region. The static bending moment which is applied in the plane of reference of the catenary is further amplified due to the imposed excitation set by the motions of the floating structure. It has been generally acknowledged that the heave motion is the worst loading condition as it causes several effects, which depending on the properties of the excitation, can be applied individually or in combination between each other. Indicative examples are the seafloor interaction, buckling-like effects, “compression loading” and heave induced out-of-plane motions. For the formulation of the seafloor interaction, various approaches have been proposed and it appears that the associated effects continue to attract the attention of the research community (Leira et al., 2004; Aubeny et al., 2006; Pesce et al., 2006; Clukey et al., 2008). “Compression loading” has been studied mainly in 2D (Passano & Larsen, 2006 & 2007; Chatjigeorgiou et al., 2007; Chatjigeorgiou, 2008), while buckling-like effects and possible

Performance Characteristics of a Tightly Moored Piston-Like Wave Energy Converter Under First- and Second-Order Wave Loads

The paper deals with the presentation of a model to predict performance characteristics of a tightly moored piston-like wave energy converter which is allowed to move in heave, pitch and sway modes of motion. The WEC’s piston-like arrangement consists of two floating concentric cylinders, the geometry of which allow the existence of a cylindrical moonpool between the external cylinder, the ‘torus’ and the inner cylinder, the ‘piston’. The first-order hydrodynamic characteristics of the floating device, i.e. exciting wave forces and hydrodynamic parameters, are evaluated using a linearized diffraction-radiation semi-analytical method of analysis that is suited for the type of bodies under consideration. According to the analysis method used, matched axisymmetric eigenfunction expansions of the velocity potentials in properly defined fluid regions around the body are introduced to solve the respective diffraction and radiation problems and to calculate the floats’ hydrodynamic characteristics in the frequency domain (Mavrakos et al. 2004, 2005). Based on these characteristics, the retardation forcing terms are calculated, which account for the memory effects of the motion. In this procedure, the coupling terms between the different modes of motion are properly formulated and taken into account (Cummins, 1962; Faltinsen, 1990). The floating WEC is connected to an underwater hydraulic cylinder that feeds a hydraulic system with pressurized oil. The performance of the system under the combined excitation of both first- and second order wave loads is here analyzed. To this end, the diffraction forces originated from the second order wave potentials are computed using a semi-analytical formulation which, by extension of the associated first-order solution, is based on matched axisymmetric eigenfunction expansions.© 2008 ASME

Nonlinear Identification and Input-Output Representation of the Modal Dynamics of Marine Slender Structures

The present work treats the problem of the dynamic behavior of a vertical slender structure subject to combined axial and transverse motions. The solution method is based on a Galerkin-type semi-analytical formulation. The responses to sinusoidal monochromatic excitation are assessed with respect to the significance of each mode and their spectral content. As a result, a reduced, yet nonlinear, lumped model for each one of the significant modes of the structure is generated. The parameters of these fixed-structure models can be determined systematically by two methods relying on the spectral analysis of the numerically calculated modal responses of the structure. The resulting models constitute an explicit input-output relationship between the imposed motions and the modes of the structure, useful for stability analysis, design and control.

Numerical and Experimental Investigation on the Dynamics of Catenary Risers and the Riser-Induced-Damping Phenomenon

Catenary risers can be equally efficient as catenary moorings in producing damping which is subsequently offered to the floating structure. Mooring-induced-damping has been investigated adequately in the recent past. The same however is not valid as far as the contribution of risers is concerned. It should be acknowledged that the main source of damping, i.e. the drag forces, is higher in risers than in moorings as the external diameter of the former is larger and the drag coefficients, at least assuming a Morison’s formula, are comparable. Therefore, the investigation of the so called riser-induced-damping phenomenon is an interesting issue. The present work is a contribution to this direction. This is performed both numerically and experimentally. For estimating damping the method proposed by Brown and Mavrakos (1999) is followed. Thus, damping due to risers is represented by the equivalent linearized coefficient the calculation of which lies on the knowledge of the energy dissipated per cycle that is calculated with the aid of the horizontal force applied at the top of the structure.Copyright