Forced vibration analysis of an offshore tower carrying an eccentric tip mass with rotary inertia due to support excitation

Dynamic responses of structures due to earthquake excitation are the important problems in engineering, thus, the information concerned is plenty. However, most of the literature is relating to the discrete methods, particularly to the finite element method (FEM), and the one relating to the method combining both the “continuous” and “discrete” models is rare. The objective of this paper is to provide some information in this respect. First, the analytical solution for the natural frequencies and normal mode shapes of a “continuous” tower, without contacting water (or “dry” tower), carrying an eccentric tip mass possessing rotary inertia is determined. Next, the partial differential equation of motion for the forced vibration of the tower, contacting water (or “wet” tower), subjected to support excitation is transformed into a matrix equation by using the last natural frequencies and normal modes shape of the freely vibrating dry tower. Finally, the numerical integration method is used to solve the matrix equation to yield the seismic response of the wet tower. In theory, the mode superposition method is correct only if the total number of modes considered approaches infinity, however, numerical results of this paper reveal that superposition of only the lowest six modes will yield excellent results to be very close to the corresponding ones obtained from the conventional FEM. For this reason, the CPU time required by the presented approach is less than 5% of that required by the conventional FEM.     

An alternative approach to the structural motion analysis of wedge-beam offshore structures supporting a load

For convenience of dynamic analysis, some offshore structures such as fixed-type platforms are often modeled as the wedge beams supporting tip lumped masses. It is well-known that, due to the effect of the surrounding water, the natural frequencies of a beam in air (or dry beam) are different from those of the same beam immersed in water (or wet beam). However, if the natural frequencies and the associated mode shapes of a dry beam are calculated by taking account of the “added mass” for the immersed beam, then the last natural frequencies and mode shapes will be equal to the corresponding ones of the wet beam. Based on the last concept, the closed form solutions for natural frequencies and the associated mode shapes of the dry beam were determined first, then the partial differential equation of motion for the wet beam was transformed into a matrix equation by using the expansion theorem and the foregoing closed form solutions of free vibration responses for the dry beam. Solving the last matrix equation will give the required natural frequencies and the associated mode shapes of the wet beam. The formulation of this paper is available for the fully or partially immersed double tapered beams with either circular, square or rectangular cross-sections. The taper ratio for width and that for depth may be equal or unequal. The numerical results of this paper were compared with the existing results or the finite-element-method results and good agreement was achieved.     

An experimental method for determining the frequency-dependent added mass and added mass moment of inertia for a floating body in heave and pitch motions

Most of the existing relevant materials have been obtained from experiments, in which evaluating the added mass at the resonant frequency corresponding to the peak of a frequency-response curve obtained from the “forced” vibration analysis is the most popular technique. In this paper, a simple experimental method was presented where the “free” vibration responses instead of the “forced” ones were used to determine the values of m_ah and I_ap. The main part of the experimental system is composed of a floating body (model) and a spring–shaft shaker. The “free” vibration of this main part was induced by imposing on it an initial displacement (and/or an initial velocity), and from the time histories of displacements information such as the “damped” natural frequencies, damping ratios, sectional added mass coefficients (C_V and C_P) were obtained. Since the displacements of the spring–shaft shaker are “translational” and those of the floating body due to pitch motions are “angular”, a technique for the transformation between the associated parameters of the two components of the main part was presented.     

Recent developments in “added-mass” planing theory

The results of several recent isolated investigations in planing theory are consolidated in this paper, together with new insights generated by a recent numerical solution of the vertically impacting wedge problem by Zhao and Faltinsen [(1992), Water entry of two-dimensional bodies. J. Fluid Mech. 246, 593–612]. As a result, in contrast to some earlier studies, it is found that the “wetted width” associated with the added mass is not that of the intersection of the wedge with the undisturbed water surface, but the wetted width of the splashed-up water, as originally proposed by Wagner [(1932), Uber Stoss-und Gleitvorgange an der Oberflache von Flussig-Keiten, Zeitschrift für Angewandte Mathematik und Mechanik, Band 12, Heft 4 (August)]. However, the splash-up ratio is not the value of (π/2–1) which he proposed, but a value which decreases with increasing deadrise, originally proposed in the late-1940s by Pierson (“Pierson's hypothesis” in the paper). For 30° deadrise, for example, Pierson's splash-up ratio is two-thirds that of Wagner's.The new equations are employed to determine the increase in the “added mass” of prismatic hull sections due to chine immersion, using experimental data. If m_o^′ is the added amss of the hull section whose chines are just wetted, Payne [(1988), Design of High-speed Boats. Volume 1: Planing. Fishergate, Inc., Annapolis, Maryland, U.S.A.] postulated that the increase in added mass due to a chine submergence (z_c) would be

where b is the chine beam and k is a constant which Payne [(1988), Design of High-speed Boats. Volume 1: Planing. Fishergate, Inc., Annapolis, Maryland, U.S.A.] gave as .The present analysis includes the “one-sided flow” correction introduced in Payne [(1990), Planing and impacting forces at large trim angels. Ocean Engng 17, 201–234]. Partly for that reason and partly because of the more precise analysis of the experimental data, the present paper revises the value to k = 2 for wetted length to beam ratios normally employed. For deadrise angles in excess of 40° and wetted keel to beam ratios in excess of 2.0, there is some evidence that k < 2.0.The revised theoretical formulation is compared with eight different sets of experimental data for flat plate and prismatic hull forms and is found to be in excellent agreement when the speed is high enough for “dynamic suction” (a loss of buoyancy at low speeds and low wetted lenghts) to be unimportant. This is true for “chines-dry” operation with deadrise angles up to 50° and chines-wet operation at length to beam ratios far in excess of the most extreme conventional practice.The research involved in performing this analysis led to the realization that different towing tanks measure different wetted chine lengths for the same hulls and test conditions. Some consistently measure more splash-up than “theory” (based on Pierson's splash-up hypothesis) predicts and others measure somewhat less than the theory. Some examples are given in Appendix B. The reason for this is not understood.     

A rapid method for recovery of data from expendable surface current probes

A sighting device, called a “probe sight”, is described which simplifies the measurement, taken, from a helicopter, of the float separations from a deployed expendable surface current probe. The separation distance between the floats (along with a known time release) is a measure of the surface current speed. The sighting device can be used at any altitude. Comparisons of the readings using the probe sight and the “normal” measurements taken from aerial photographs for 180 stations in the Chukchi Sea, show that the difference between the two methods is less than 10% when the current speed is greater than 10 cm sec⁻¹. The largest difference (15%) occurs at those stations where the current speed is less than 10 cm sec⁻¹.     

Transient effects in wave-current boundary layer flow

Previous studies of combined wave and current bottom boundary layer flow have concentrated on the final converged state of the flow following the addition of waves to a current. While this final state is of primary interest to modellers and engineers, it pre-supposes that such a state is actually attained in reality, and this may not always be the case. In addition, it overlooks the interesting and complicated transient effects which occur as a wave-current flow evolves from one state to another. The present study concentrates attention on the transient effects predicted by a “one-equation” turbulence closure model. Results of case studies are presented in which waves are superimposed co-linearly on a current (“forward problem”), and are then removed from the converged wave-current flow (“backward problem”). Two formulations of the “forward” and “backward” problems are discussed. In the first the steady component of the pressure gradient driving the mean flow is held constant throughout, and in the second the steady component of the mass flux is held constant. In each case the detailed evolution of the profiles of mean velocity, turbulent energy, mixing length, eddy viscosity and shear stress are discussed. More generally, the question of the convergence timescale of a combined wave-current flow is considered, and a convergence criterion is proposed.     

Analytical intercomparison results from the 1990 Intergovernmental Oceanographic Commission open-ocean baseline survey for trace metals: Atlantic Ocean

“Dissolved” (< 0.4 μm filtered) and “total dissolvable” (unfiltered) trace element samples were collected using “clean” sampling techniques from four vertical profiles in the eastern Atlantic Ocean on the first IOC Trace Metals Baseline expedition. The analytical results obtained by 9 participating laboratories for Mn, Fe, Co, Ni, Cu, Zn, Cd, Pb, and Se on samples from station 4 in the northeast Atlantic have been evaluated with respect to accuracy and precision (intercomparability). The data variability among the reporting laboratories was expressed as 2 × SD for a given element and depth, and was comparable to the 95% confidence interval reported for the NASS seawater reference standards (representing analytical variability only). The discrepancies between reporting laboratories appear to be due to inaccuracies in standardization (analytical calibration), blank correction, and/or extraction efficiency corrections.Several of the sampling bottles used at this station were not adequately pre-cleaned (anomalous Pb results). The sample filtration process did not appear to have been a source of contamination for either dissolved or particulate trace elements. The trace metal profiles agree in general with previously reported profiles from the Atlantic Ocean. We conclude that the sampling and analytical methods we have employed for this effort, while still in need of improvement, are sufficient for obtaining accurate concentration data on most trace metals in the major water masses of the oceans, and to enable some evaluation of the biogeochemical cycling of the metals.     

Hydrocarbons in the Bay of Bengal and Central Indian Basin bottom sediments: indicators of geochemical processes in the lithosphere

A study on the bulk distributions and molecular structures of n-alkanes and polycyclic aromatic hydrocarbons (PAH) in organic matter of the sediments from the Bay of Bengal and the Eastern and Central Indian Basins was undertaken. The former two regions represent areas characterised by “normal” sedimentation while the third one mainly represents a region of “active tectonism”. Content of the hydrocarbons in the sediments of “normal” sedimentation ranges between 4.6 and 10.5 μg/g and aromatic hydrocarbons ranges between 0 and 0.38 μg/g. n-Alkanes in the sediments of the northern deep part of the Bay of Bengal consist mostly of long-chain structures (total C₂₅–C₃₃ up to 70%) with a high carbon preference index (CPI=3.01–3.43), indicating a large contribution of organic matter from terrigenous sources. The sediments from the Eastern Indian Basin have n-alkane distributions in which the long-chain components did not exceed 52.5% and the CPI was 1.7–1.90, indicating that the hydrocarbons are mostly derived from marine sources. Sharp increases of hydrocarbons are found in the vicinity of the tectonically active region of the Central Indian Basin, particularly in the sediments collected from the fracture zone. The total concentration of hydrocarbons increase to 170 μg/g and the aromatic hydrocarbons fraction to 156.3 μg/g. The proportion of short-chain n-alkanes increases up to 70%, CPI decreases to 0.76–1.12, and high concentrations of n-C₁₆ (16–40%) occur, all of which are absent in the other samples. The molecular content of PAH includes the unsubstituted individual structures: biphenyl, fluorene, pyrene, perylene, benzo(ghi)perylene, and the groups of homologues of naphthalene, benzofluorene, phenanthrene and chrysene. The association of the PAH and composition of paraffin hydrocarbons in the surficial sediments of deformation zone indicate that these are the resultant products of hydrothermal processes. It is, therefore, suggested that the association and composition of the hydrocarbons in sediments can be utilised as a paleoceanographic parameter to decipher the history of tectonism of an area.     

Transport timescales for identifying seasonal variation in Bass Strait, south-eastern Australia

A three-dimensional σ-coordinate ocean model with realistic forcing is used to derive and compare flushing time, residence time and water age distributions in Bass Strait, a broad shallow shelf sea in south-eastern Australia which exhibits seasonal variation in water mass properties and circulation. Results illustrate flushing out of most old water occurs each winter–spring period and the circulation in summer increases age of remnant older water in the Strait. A correlation between water age and salinity is found in winter which is the result of advective “erosion” of the interior water mass. The presence of an area in the south-eastern part of the interior with low flushing is suggested to result from a number of physical factors including the presence of quasi-stationary eddies which entrain age, leading to relatively older water residing there.     

An efficient algorithm for strapdown accelerometer-based motion measurement

The paper is concerned with the measurement of motion of free floating bodies using accelerometers strapped to a cross-arm mounted on the body. The measurement system has been studied with the help of a formulation involving a set of coupled nonlinear initial-value equations involving the angular acceleration components. A PC-based software using the Bulirsch-Stoer technique has been developed to solve the initial-value problem so as to deduce the body motions from the measured accelerations. Suitable filtering strategy has been employed at every stage of numerical integration. The reliability of the strapdown accelerometer system together with software developed has been validated using a “dry” test. Typical motion measurements have been done in all the six degrees of freedom of a tug model in a wave flume. The method is deemed to be an efficient and cost-effective technique suitable for free floating bodies and for large motions.     

Advanced characterization of marine dissolved organic matter by combining reversed-phase liquid chromatography and FT-ICR-MS

Marine dissolved organic matter (DOM) was separated by reversed-phase (RP) liquid chromatography method and analyzed with fluorescence/absorption detection and Fourier transform ion cyclotron mass spectrometry (FT-ICR-MS). The three key characteristics of the RP method are: (a) The C18-RP column chosen provides enhanced separation when the aqueous phase is 100% buffer-free water, and it does not degrade over time; (b) the water eluent adjusted to pH 7 significantly improves the resolution of water soluble compounds; (c) the initial flow maintained at low levels improves the separation of polar compounds. In samples, containing “fresh” DOM, specific peaks were detected, which were absent in “old” DOM samples. The combination with size exclusion chromatography (SEC) also demonstrated the relation between polarity and molecular size of DOM. FT-ICR-MS was applied to evaluate the quality of separation on a molecular scale demonstrating that physico-chemical characteristics of DOM can be related to molecular formulas. Sample extracts were separated into 4 preparative fractions, and a large suite of the identified molecular formulas only occurred in specific fractions. This is an important basis for the application of further analytical techniques in order to perform a more target-oriented analysis aiming at the determination of source and process biomarkers for DOM.     

Total (practical) stability of ships

In this paper the “total (practical) stability” concept is introduced to nonlinear forced rolling motion of a ship. This is achieved by employing “boundedness” and “Lyapunov's function” approach. In this respect two new theorems are proved and conditions and domain of Practical Stability are evaluated. The Paper also contains a critical review of the present status of international intact ship stability regulations. A qualitative discussion of oscillatory rolling motion and the capsizing phenomena is presented.     

Multi-vessel seakeeping computations with linear potential theory

The wave-induced motion of two vessels in close proximity is studied using traditional two-dimensional (2D) and three-dimensional (3D) boundary element methods. Added mass, damping, and the behavior of the free surface between the vessels are examined in some detail. As expected based on previous work, the response of the water between the vessels is found to have a profound effect on the hydrodynamic forces. At “critical frequencies” corresponding to standing waves between the hulls, the hydrodynamic forces undergo significant drastic changes. The 2D and 3D results are compared, and the effects of a skew angle between the vessels are examined. Some of the consequences of the behavior at the critical frequencies for simulations in the time domain are examined, the most significant of which is a very lightly damped impulse response.     

A discus-hulled wave measuring buoy

Described herein is a self-contained, discus-hulled buoy 1.5 m dia., weighing 150 kg, which uses inertial instruments to measure wave height and tilt. Wave tank calibration and the theory of shallow draft buoys demonstrate such a hull accurately follows waves with length greater than twice the buoy diameter. The non-linear response of the buoy determines its sensitivity to low-frequency waves in a sea. And the ratio of wave signal to instrument “noise” is constant over the energetic part of the ocean-wave spectrum for measurements of wave acceleration and slope.     

Static and dynamic aspects of a capsize phenomenon

Capsizing of ships constitutes a primary group of casualties that leads to loss of life and money. Unfortunately, its mechanism has yet to be fully resolved due to underlying complex dynamics and parameters. Upon studying the causes in more detail, designing safer ships against capsizing may become a reality. In the present study, a relatively different approach called “reserve of stability” or “stability margins” which utilizes both statical and nonlinear dynamical aspects of stability is employed to analyze ship hydrodynamics. For this purpose a nonlinear roll model in beam waves has been implemented. In order to apply the theory, a capsized vessel is chosen to be analyzed in terms of stability. The necessary data about the vessel at the time of capsizing were collected from the published work found in the naval architecture literature. Suggestions are made based on the results of the analysis to improve ship stability qualities in a seaway.     

Propulsion of single-screw ships

On the basis of the little clause in the “Outline Specification” for a new ship: “Trial speed at a load draught of … with the engine at maximum continuous rating has to be …” some aspects regarding propulsion of single-screw ships are discussed, especially the problem of how to combine the hull form, the propeller and the machinery for propulsion in such a way that an optimal solution is obtained.In order to limit the problem, only ships provided with a single conventional propeller for propulsion are considered.A parameter study of a single-screw vessel has been done in order to get some concrete information on the interaction between ship, engine and propeller, and to investigate how the ship propeller power curve should be placed in relation to the engine operation area and to investigate changes in this relationship when the conditions change.     

Tracking the last sea-level cycle: seafloor morphology and shallow stratigraphy of the latest Quaternary New Jersey middle continental shelf

Seafloor geomorphology and surficial stratigraphy of the New Jersey middle continental shelf provide a detailed record of sea-level change during the last advance and retreat of the Laurentide ice sheet (120 kyr B.P. to Present). A NW–SE-oriented corridor on the middle shelf between water depths of 40 m (the mid-shelf “paleo-shore”) and 100 m (the Franklin “paleo-shore”) encompasses 500 line-km of 2D Huntec boomer profiles (500–3500 Hz), an embedded 4.6 km² 3D volume, and a 490 km² swath bathymetry map. We use these data to develop a relative stratigraphy. Core samples from published studies also provide some chronological and sedimentological constraints on the upper <5 m of the stratigraphic succession.The following stratigraphic units and surfaces occur (from bottom to top): (1) “R”, a high-amplitude reflection that separates sediment >46.5 kyr old (by AMS ¹⁴C dating) from overlying sediment wedges; (2) the outer shelf wedge, a marine unit up to 50 m thick that onlaps “R”; (3) “Channels”, a reflection sub-parallel to the seafloor that incises “R”, and appears as a dendritic system of channels in map view; (4) “Channels” fill, the upper portion of which is sampled and known to represent deepening-upward marine sediments 12.3 kyr in age; (5) the “T” horizon, a seismically discontinuous surface that caps “Channels” fill; (6) oblique ridge deposits, coarse-grained shelly units comprised of km-scale, shallow shelf bedforms; and (7) ribbon-floored swales, bathymetric depressions parallel to modern shelf currents that truncate the oblique ridges and cut into surficial deposits.We interpret this succession of features in light of a global eustatic sea-level curve and the consequent migration of the coastline across the middle shelf during the last 120 kyr. The morphology of the New Jersey middle shelf shows a discrete sequence of stratigraphic elements, and reflects the pulsed episodicity of the last sea-level cycle. “R” is a complicated marine/non-marine erosional surface formed during the last regression, while the outer shelf wedge represents a shelf wedge emplaced during a minor glacial retreat before maximum Wisconsin lowstand (i.e., marine oxygen isotope stage 3.1). “Channels” is a widespread fluvial subarial erosion surface formed at the late Wisconsin glacial maximum 22 kyr B.P. The shoreline migrated back across the mid-shelf corridor non-uniformly during the period represented by “Channels” fill. Oblique ridges are relict features on the New Jersey middle shelf, while the ribbon-floored swales represent modern shelf erosion. There is no systematic relationship between modern seafloor morphology and the very shallowly buried stratigraphic succession.     

Study on the dynamic characteristic of a U-type tuned liquid damper

By means of Lagrange's equation, the “coupled” equations of motion for a horizontal plate carrying a U-type tuned liquid damper (TLD) are derived. The “uncoupled” equations of motion for the liquid (in the TLD) and the structural system are then obtained by decoupling the “coupled” ones. Unlike the existing literature to indirectly determine the natural frequencies of a damped vibrating system by using the resonant method, the “complex” eigenvalues of the coupled damped system are obtained directly from the associated eigenvalue equations. Besides, the pressure intensities in the two air chambers and the sizes of the two vertical tanks together with the horizontal conduit are arbitrary in the formulation of this paper. The influence of some key parameters of the TLD on the dynamic responses of the structural system is studied.