Nonlinear Dynamic Response of a Compliant Tower Under the Effect of Steady and Unsteady Sea States

The purpose of this work is to highlight the importance of considering the actual nonlinear dynamic response for the analysis and design of fixed deep water platforms. The paper highlights the necessity of applying dynamic analysis through the comparison with the results obtained by the authors by applying static nonlinear analysis on the structure under examination. The example treated in the context of the present paper is a compliant tower, set-up in deep water. Nonlinearities are considered both for the calculation of the wave loadings and the structural analysis. The wave loading is based on linear random wave theory and comparisons are provided with the steady wave theories, Airy and Stokes 5th. The former solution is based on the most probable shape of a large linear wave on a given sea-state; the auto-correlation function of the underlying spectrum. On the other hand, in the field of structural analysis, two cases are considered for comparison, static analysis and time history dynamic analysis. For both types of analysis, two sub-cases are considered, a case in which geometric nonlinearity and nonlinearities related to the modelling of the soil are considered and a case in which the corresponding linear theories are employed (reference cases). The structural calculations were performed using the well-known structural analysis software SAP2000, which was enhanced by a special programming interface that was developed to calculate the wave loading and to directly apply the generated loads on the structural members. The results show that the consideration of the particle velocities associated with the linear random wave theory in the wave loading lead to significant differences with respect to the steady wave theories in terms of the displacements and stresses of the structure. Moreover, irrespectively of the adopted wave theory, the nonlinear analyses lead to significant discrepancies with respect to the linear ones. This is mainly associated with the nonlinear properties of the soil. Another source of discrepancies between the results of static and dynamic analyses stems from the change of the effective natural frequency of the structure when nonlinearities are considered.

Free and Forced Vibration Analysis of an Idealized Compliant Tower With Superstructure, due to Current Loads, Wave Excitation, and Earthquake Impulses

A compliant tower (CT) is modeled as a partially dry, partially tapered, damped Timoshenko beam with the superstructure modeled as an eccentric tip mass, and a non-classical damped boundary at the base. The foundation is modeled as a combination of a linear spring and a torsional spring, along with linear and torsional dampers. The mean empty space factor due to the truss type structure of the tower is included. The effect of shear deformation and rotary inertia are included in the vibration analysis; with the non-uniform beam mode-shapes being a weighted sum of the uniform beam mode-shapes. The weights are evaluated by the Rayleigh-Ritz method, using the first ten modes and verified using Finite Element Method (FEM). The superstructure adds to the kinetic energy without affecting the stiffness of the beam, thereby reducing the natural frequencies. The weight of the superstructure acts as an axial compressive load on the beam, reducing its frequencies further. Kelvin-Voigt model of structural damping is included. A part of the structure being underwater, the virtual added inertia is included to calculate the wet natural frequencies. The CT is first subjected to steady current loads of a given velocity profile. The static deflection and overturning moment is estimated for current loads. The CT is then studied for wave excitation at various seas states. Morrison’s equation and Pierson-Moskowitz Spectrum are used to derive the forces for different sea states. The forced vibration analysis of the structure is done via Rayleigh-Ritz method and verified using FEM. The maximum horizontal deflection and shear stress of the base of the superstructure, and the normal/shear stresses at the foundation are analyzed. Finally, the CT is subjected to earthquake excitation, modeled as an arbitrary horizontal impact excitation at the base. The above forced vibration analysis is repeated.

Float Over Installation Method—Comprehensive Comparison Between Numerical and Model Test Results

Installing a large deck onto a platform, such as a spar, using the floatover method is gaining popularity. This is because the operational cost is much lower than other methods of installation, such as modular lifts or a single piece installation by a heavy lift barge. Deck integration can be performed on land, at quay side and will not depend on a heavy lift barge. A new concept for a floatover vessel has been developed for operations in the Gulf of Mexico and West Africa. In this application sea state conditions are essential factors that must be considered in the Gulf of Mexico, especially for transportation. In West Africa, swell conditions will govern floatover deck (FOD) installation. Based on these two different environmental conditions, Technip Offshore, Inc. developed the FOD installation concept using semi-submersible barge type vessels. A significant amount of development work and model testing has been done on this method in recent years on spar floatover. These tests have validated our numerical methods. Another test was conducted to investigate the feasibility of a deck float-over operation onto a compliant tower for a West Africa project. The project consists of a compliant tower supporting a 25,401metricton(28,000s.ton) integrated deck. This paper will describe comparisons between model test data and numerical predictions of the compliant tower floatover operation.

Float Over Installation Method: Numerical and Model Test Data

Installing a large deck onto a platform, such as a spar, using the floatover method is gaining popularity. This is because the operational cost is much lower than other methods of installation, such as modular lifts or a single piece installation by a heavy lift barge. Deck integration can be performed on land, at quay side and will not depend on a heavy lift barge. A new concept for a floatover vessel has been developed for operations in the Gulf of Mexico and West Africa. In this application sea state conditions are essential factors that must be considered in the Gulf of Mexico, especially for transportation. In West Africa, swell conditions will govern floatover deck (FOD) installation. Based on these two different environmental conditions, Technip Offshore Engineering developed the FOD installation concept using semi-submersible barge type vessels. A significant amount of development work and model testing has been done on this method in recent years on spar floatover. These tests have validated our numerical methods. Another test was conducted to investigate the feasibility of a deck float-over operation onto a compliant tower for the Benguela Belize (BBT) project. The BBT project consists of a compliant tower supporting a 25,401 metric ton (28,000 s. ton) integrated deck. This paper will describe comparisons between model test data and numerical predictions of the compliant tower floatover operation.

Nonlinear Coupled Transverse and Axial Vibration of a Compliant Structure: Free and Forced

A compliant tower in the ocean environment is modeled as a beam undergoing coupled transverse and axial motion. The beam is supported by a torsional spring and has a point mass at the other end. It is assumed that the strains are small but the rotation is moderate compared to the strain so that the equations of motion for the axial and transverse motion are nonlinearly coupled. The nonlinear coupled equations of motion are derived here using Hamilton’s principle. The forced responses due to random waves are observed here. The responses are obtained numerically using the finite difference approach.