Jack Y.K. Lou

DYNAMIC COUPLING OF A LIQUID-TANK SYSTEM UNDER TRANSIENT EXCITATIONS

Abstract It has been observed that the unrestrained free surface of a container can create relatively large liquid movements for even very small motions of the container. This excessive movement may endanger the stability as well as the maneuvering quality of the transporting vehicle. Therefore, the effects of the dynamic coupling of a liquid-tank system are of great concern. This dynamic coupling problem is studied analytically for a two-dimensional, rectangular rigid tank with no baffles. The governing equations of the liquid motion are derived with reference to a moving coordinate system which is fixed to the moving container. With the liquid forces generated by the fluid motion as the external exciting force for the tank, the motions of the liquid-tank system can be described according to Newtons Second Law of Motion. By using the Laplace transformation technique, the dynamic responses of the coupled system can be examined in detail. Numerical results for various types of external excitations and the resultant motions of the fluid-tank system are presented and compared with the equivalent non-shifting cargo system. The results of the comparison indicate that the discrepancy of responses in the two systems can obviously be observed when the ratio of the natural frequency of the fluid and the natural frequency of the tank is close to unity. Also, the amount of fluid inside the tank is a very important factor in determining the responses.

Non-linear behavior and chaotic motions of an SDOF system with piecewise-non-linear stiffness

Abstract Forced vibrations of a single-degree-of-freedom system with unsymmetric, piecewisenon-lincar restoring forces are investigated using direct numerical integration and approximate analytical methods. A simple and efficient algorithm was developed to analyse the piecewisenon-linear system by the harmonic balance method and fast Fourier transformation technique. The highly non-linear characteristics, including subharmonics, instabilities, bifurcations, Lyapunov exponents and domain of attraction, were examined. Possible occurrence of chaotic motion was investigated by means of direct numerical integration and the classical stability theory with the aid of Hills type equation. It is found that the threshold of the onset of chaotic motion is very sensitive to any changes in system parameters, and chaotic motion will occur as the excitation amplitude exceeds certain limits.

EFFECTS OF RIGIDITY AND INTERNAL FLOW ON MARINE RISER DYNAMICS

A mathematical model for the lateral motion of a marine riser is developed to examine the effect of the internal flow and bending rigidity of the pipe on the dynamic behaviour of the riser. The model includes a steady flow inside the pipe together with other factors such as currents, wave excitation, rig motions, etc. A singular perturbation technique is used to solve the equations of the mathematical model for the risers with a relatively small elastic rigidity. The solution is expressed as the superposition of three components; they are (1) the static displacement due to the current and mean rig offset, (2) the time-dependent component due to the rig sway or surge motion, and (3) the forced vibration which accounts for inertia effects and time-dependent fluid interaction forces. It is found that the internal flow acts to reduce the effect of the top tension. However, its effect on riser dynamics is not significant when the top tension of the riser is relatively high. For small top tension cases, the perturbation technique is no longer valid and the effect of internal flow on riser dynamics remains to be investigated.

NONLINEAR BEHAVIOUR OF AN ARTICULATED OFFSHORE LOADING PLATFORM

An analytical model was developed for the dynamic analysis of an articulated loading platform (ALP) under regular wave excitations. The dynamic response and stability of the ALP tower, treated as a single-degree-of-freedom system, was investigated with direct numerical integration and approximate analytical methods. The highly nonlinear characteristics, including subharmonics, instabilities, period-doubling bifurcations and Lyapunov exponents, were examined. Possible occurrence of chaotic motion was investigated by means of direct numerical integration and application of the classical stability theory with the aid of Hills type equation. It was discovered that for the parameters studied, chaotic motion with only take place under the action of a train of extremely large waves. Such motion may develop either through period-doubling bifurcations or take place suddenly depending on the excitation amplitude.

Stability of vortex-induced oscillations of tension leg platform tethers

Abstract The study concerns possible occurrence of instability and bifurcation of vortex-induced transverse oscillations for tension leg platform tethers. The tether is modeled by a simple nonautonomous system with quadratic damping and parametric excitation. Krylov-Bogoliubov-Mitropolsky method was used to predict the stability of the system. Regions of unstable solutions, phase plane portraits and Poincare maps were constructed to illustrate the response of the tether.

Model identification and control of a tuned liquid damper

Experimental studies have been conducted to investigate the feasibility of using active control of the tuned liquid damper for reducing the vibration of large civil structures. The results indicate that a simple mechanism can be designed to actively control the tuning of the system by adjusting the length of the liquid tank with rotatable baffles driven by stepping motors. The tank can be permanently installed and no powerful actuators would be required to regulate its motion. As a result, the system can be built inexpensively and can be tested frequently to ensure its reliability. A control strategy based on detection of frequency content and two-state control is simple and can be easily implemented in a microprocessor. Preliminary results of the damper model identification are provided, allowing computer simulations and the design of advanced control strategies for fine tuning of the liquid damper in future studies. The performance of this novel damper is verified by computer simulations and experiments using a physical model.

Vortex-induced nonlinear oscillation of tension leg platform tethers

Abstract The paper concerns the nonlinear oscillation of tension leg platform tethers induced by vortex shedding in a combined wave and current field. Quadratic damping and parametric excitation are included in the mathematical model. Only the vortex-induced oscillations normal to the wave and current are considered. However, the method used can also be applied to study the in-line oscillations due to waves. Stability analysis of the nonlinear system will be presented in a separate paper. A multiple-term Galerkins method is used in the numerical computations. Results for the CONOCOs Hutton TLP are presented to illustrate the importance of multiple-term solutions under lock-on conditions. The effects of the drag and lift coefficients and the frequencies of the waves and parametric excitations have also been investigated.

Nonlinear mooring line induced slow drift motion of an ALP-tanker

Abstract A tanker moored to an articulated loading platform (ALP) is modeled by a 2-DOF system. The mooring line between the ALP and tanker is represented by an unsymmetric, piecewise-nonlinear restoring function. Forced vibrations of this system are investigated using direct numerical integration. The highly nonlinear characteristics, including multiple solution, subharmonics, and bifurcations are discussed. Slow drift oscillation could occur under harmonic excitations due to nonlinearities of the systems. The sensitivity of the dynamic response of the strong nonlinear system with respect to system parameters and initial conditions is examined.

THE HYDROELASTIC EFFECTS ON THREE-DIMENSIONAL STRUCTURAL DYNAMICS

Abstract In a previous article by the present authors, a three-dimensional numerical technique was developed for determining the wave-exciting and motion-induced hydrodynamic forces for fixed and floating structures in a fluid of finite or infinite depth. The analysis was carried out within the framework of linear diffraction theory and direct boundary-element method for rigid bodies of arbitrary shape. In the present paper the effects of structural flexibility are considered, and the solution of the hydroelastic problem is obtained by employing the direct boundary-element method for the fluid and the finite-element method for the structure. The fluid potential is expressed by means of a Helmholtz integral, which involves the normal velocities of the fluid and their derivatives at the fluid-structure interface. Upon discretizing the integral equation by using constant or linear elements and by enforcing the velocity continuity condition at the discrete points of the interface, the fluid potential can be related to the elastic and inertia properties of the structure. Solution of this set of complex linear simultaneous equations then yields the potential function at the interface nodal points. The fluid and structural motions can then be readily calculated. A computer program based on this approach is developed to calculate motion-induced hydrodynamic forces. As an example, the relationship between the hydrodynamic force and the stiffness of the structure is examined by evaluating the hydrodynamic forces and vibration characteristics of a box structure with a flexible bottom plate in semi-infinite and infinite fluid. As expected, the hydrodynamic force increases with increasing flexibility and the hydroelastic effect also increases with increasing exciting frequency. Natural frequencies of the bottom plate in heaving motion are also determined. Results show that the hydrodynamic load affects natural frequencies of the structure in both the fundamental and higher modes.

DYNAMIC RESPONSE OF A TANKER MOORED TO AN ARTICULATED LOADING PLATFORM

Abstract An analytical model was developed for the dynamic analysis of an articulated loading platform in an operation condition, while remaining in a head seas position. The environmental excitation considered, resulting from groups of regular waves, included first- and second-order force contributions. The nylon hawser connecting the tanker to the ALP was modeled as a nonlinear spring. The hydrodynamic load on the tower was evaluated using Morisons equation, which was modified to account for the relative motion of the tower and the fluid particles. The hydrodynamic load on the tanker was calculated using linear diffraction theory based on the 2-D Helmholtz equation. The “near field” approach of Pinkster was used to evaluate the drift force.