bluuebunny/crossref_metadata_2025 huggingface dataset:
Global Static Instability of Risers
Authors: Bernitsas Michael M. , Kokkinis Theodore
Published: January 2021

Global instability of risers depends on riser weight, internal and external fluid static pressure forces, tension exerted at the top of the riser, and boundary conditions. The purpose of this work is to study the effects of these factors on the stability boundaries of risers and specifically.(i) compare buckling loads for various boundary conditions; (ii) find the long-riser instability behavior from the asymptotics of the stability boundaries; (iii) find the short-riser instability behavior; (iv) analyze the relative effects of boundary conditions, weight, internal pressure, and bending rigidity on stability; (v) show the variation of the stability boundary shape with the order of the buckling mode; and (vi) compare the critical length at which risers in tension over their entire length may buckle due to internal pressure, for various boundary conditions.
Analysis of Riser Measurements in the North Sea
Authors: Verbeek P. H. J.
Published: January 2021

Riser measurements in the field have provided a variety of data collected from several locations in the North Sea. Data were obtained by means of instrumented riser joints installed in both a 24-in. and a 16-in. drilling riser. Bending moments in the riser, riser tensions, motions of the semisubmersible, and wave heights were recorded simultaneously. The measurement program was aimed at verifying predictions from theoretical riser models in the typical regions of riser response; namely, the wave-active zone at the top, the "boundary layer" at the bottom, and the riser main section in between. In this paper attention is focused on the data obtained for riser response in the wave-active zone. Measured results are compared with theoretical predictions based on both analytical solution methods and numerical time-domain simulation techniques. In particular, the relationship between the standard deviation of riser bending response and significant wave height is discussed, as is the probabilistic nature of riser response. It is concluded that standard deviations of measured bending moment response agree well with theoretical results. The probability distributions of measured response were found to be non-Gaussian and consistent with theoretical predictions based on Morison-type wave loading.
A Finite-Element Solution of Thermal Distortion with Applications to Thrust Bearings
Authors: Ma James H.
Published: January 2021

A finite-element code to account for thermal expansion in a solid was developed for the Independent Research and Independent Exploratory Development project "Tribology of Sliding Surface Bearings." The program is based on a two-dimensional model using a second or higher-order interpolation function in the element space that will allow a diverse temperature field, such as a steep nonlinear temperature gradient, to be prescribed in a solid body. The computer code has a definite advantage over certain finite-element systems that are commercially available. Many accept only a constant, or averaged, temperature input into their element space. With the new capabilities, complex thermal mechanical responses under severe temperature gradients can be readily analyzed. For instance, the hot spot in a ship's landing deck due to the concentrated heat load, such as those generated by high-temperature jet exhaust, can be more realistically represented by the elements of current development. The element mesh size and the input data set are more manageable.
On the Theory of Peripheral Jets in Proximity to the Ground
Authors: Tselnik David
Published: January 2021

The theory of plane, inviscid, incompressible, peripheral jets in proximity to the ground is set forth. An approach to the problem aimed at obtaining rapidly enough convergent thin-jet infinite series solutions and sound thin-jet asymptotics is pointed out. For a number of important special cases, the solutions as infinite series are found. The thin-jet approximate solution (as the first three terms of the corresponding infinite series) valid in the most general case is found. Approximations of the flow under consideration by means of annular flows are studied.
Numerical Study of a Slender-Ship Theory of Wave Resistance
Authors: Noblesse Francis
Published: January 2021

This study is a continuation of the previous numerical study by Chen and Noblesse [1]2 of the slender-ship theory of wave resistance presented in Noblesse [2]. Results of systematic calculations of wave resistance are presented for three simple sharp-and round-ended strut-like hull forms having beam/length and draft/length ratios equal to 0.15 and 0.075, respectively. Numerical results are presented for the first order slender-ship approximation and for seven closely related wave-resistance approximations. The nondimensional wave-resistance values associated with these eight approximations are plotted versus the Froude number in the range 1 ≥ F ≥ 0.18. The Kochin wave-energy function corresponding to four approximations is also depicted for three Froude-number values. The wave potential is shown to have more pronounced effects upon the wave resistance, causing large phase shifts in particular, than the nonoscillatory near-field potential. A simple analytical approximation to the near-field term in the Green function is proposed. Finally, theoretical predictions are compared with experimental data for the Sharma strut and the Wigley hull.
The Drag at Ship Scale of Planes Having Any Quality of Roughness
Authors: Grigson Christopher
Published: January 2021

A method for determining the drag at full scale of flat surfaces having any quality of roughness is explained. The method is partly experimental, partly theoretical. The dimensionless velocity drop caused by the roughness is measured at laboratory scale; it depends on two parameters of the roughness and is expressed in terms of a power series in these parameters. The theory then enables the drag coefficients to be calculated at full scale. The degree of physical approximation of the theory is that of the boundary-layer equation itself; the mathematical basis is exact; and the experimental accuracy is that of the measurements of the velocity loss function. The question of units for the roughness parameters is discussed and is shown to be important if the results are to be applied. Examples of many different kinds of surface are analyzed, of relevance both to the drag of propellers and to the hulls of very rough ships. Attention to the quality of the roughness could lead to appreciable reductions in the drag of propeller blades.
Probabilistic Analysis of the Combined Slamming and Wave-Induced Responses
Authors: Ferro G. , Mansour A. E.
Published: January 2021

The success of implementing reliability analysis in structural design depends to a large extent on the ability to combine the loads acting on the structure, and on extrapolating their magnitudes to obtain the extreme value of the total combined load. In this paper, a new theory is proposed to combine the slamming and wave-induced responses of a ship moving in irregular seas. The slamming and wave-induced responses are both considered as stochastic processes, and the properties of the combined response are determined on that basis. The slamming loads alone are considered as a train of impulses of random intensity and random arrival time as has been shown by Mansour and Lozow [1],3 but the dependence between the intensity and arrival time is considered in the stochastic modeling. The extreme value of the combined response is then investigated for use in design applications. An example of application to a cargo ship is given and a sensitivity analysis is conducted to determine how sensitive the results are to some of the important input parameters.
A Mathematical Model for Optimal Strength and Alignment of a Marine Shafting System
Authors: Mourelatos Zissimos , Papalambros Panos
Published: January 2021

The design of a marine shafting system is modeled mathematically in order to perform optimization studies with respect to shaft strength as well as longitudinal and vertical positioning of the bearings. The objective criteria used are minimization of the bearing reaction influence numbers and even distribution of the bearing loading. Design trade-offs can be thus established. The problem is posed in a nonlinear programming formulation and is solved using a standard generalized reduced gradient method (GRG2), but in a specialized solution strategy. Two examples from actual ship designs are presented.
The Water Column Oscillation in a Duct Between Two Half Ship Section Barriers
Authors: Lee B. S. , Day A. H.
Published: January 2021

The oscillation of a water column in a duct between two half ship section barriers is relevant to several practical applications, notably wave energy devices and moonpools for the launch/retrieval of subsea units from diving support vessels. The oscillation is solved for the case where the barriers are space fixed, and the method used is then extended to include effects due to the heave motion of the barriers. Results obtained in the form of response amplitude operators indicate that the water column oscillation demonstrates a distinct peak response, and that the key parameter controlling this response is the ratio of duct width to barrier draft.
Numerical Evaluation of the Green Function of Water-Wave Radiation and Diffraction
Authors: Telste J. G. , Noblesse F.
Published: January 2021

This study presents a simple, accurate, and efficient method for numerically evaluating the Green function, and its gradient, of the theory of water-wave radiation and diffraction. The method is based on five expressions for the Green function that are useful in complementary regions of the quadrant in which the Green function is defined. These expressions consist of asymptotic expansions, ascending series, two complementary Taylor series, and a numerical approximation based on a modified form of the Haskind integral representation. The four series representations are refinements of the series obtained previously in Noblesse [1].2 These series express the Green function and its gradient as sums of power series and terms involving functions of only one variable. The power series can be evaluated quickly by using recurrence relations; and the functions of one variable, by using rational approximations. The method permits the Green function and its gradient to be evaluated with an absolute error smaller than 10–6 very efficiently (with computing time less than 6 × 10–5 sec on a CDC CYBER 176 computer). A listing of the FORTRAN subroutine is included in the paper.
Effect of Shallow Water on a Mathematical Hull at High Subcritical and Supercritical Speeds
Authors: Millward A. , Bevan M. G.
Published: January 2021

Experiments have been made in a towing tank to measure the resistance of a mathematical hull form in deepwater and in shallow water at high subcritical and supercritical speeds. The data have been compared with calculations using linearized wave theory for the same hull shape. The results have shown fairly good agreement, with the greatest differences occurring near the subcritical resistance peak.
Theory of Short Wave Excitation
Authors: Chung Yong Kwun
Published: January 2021

When the wavelength of the incident wave is short, the total surface potential on a floating body is found to be 2∅ i & O (m-l∅ i) on the lit surface and O (m-l∅ j) on the shadow surface where ~b i is the potential of the incident wave and m the wave number in water of finite depth. The present approximation for wave exciting forces and moments is reasonably good up to X/L ∅ 1 where h is the wavelength and L the characteristic length of the body.
Time-Periodic Wave Loading on a Submerged Circular Cylinder in a Current
Authors: Grue John
Published: January 2021

The time-periodic pressure loading, added mass, damping, and exciting forces on a horizontal submerged circular cylinder in a current are examined. The fluid layer is infinitely deep and the motion is two-dimensional. The boundary-value problem is solved by applying a source distribution along the contour of the body. The forces become finite for τ = Uσlg approaching 1/4 (where U is the speed of the current, σ the frequency, and g the acceleration due to gravity). The added-mass force becomes negative for τ close to 1//4. The damping force is very small for τ > 1/4. The exciting loading on the cylinder is larger for incoming waves traveling against the current than for incoming waves traveling with the current.
Hydrodynamically Coupled Motions of Two Ships Advancing in Oblique Waves
Authors: Fang M. C. , Kim C. H.
Published: January 2021

An analytical investigation is carried out on the wave-induced motions on two closely spaced, hydrodynamically interacting slender bodies advancing in oblique waves. The two-dimensional procedure, including the hydrodynamic interaction and an integral equation method, is utilized. Numerical results are presented for the coupled motions of two ships. Comparisons are made with the behavior of a monohull and the interaction effect is found to be very important. Different headings and speeds are investigated. It has been found that the rolling motion is reduced while the ships are advancing—a helpful circumstance for cargo transfer between two ships. This study shows that the strip method is a useful technique to predict the hydrodynamically coupled motions between two ships advancing in oblique seas.
Post-Buckling Behavior of Pressurized Long Circular Cylindrical Shells
Authors: Bert Charles W. , Birman Victor
Published: January 2021

The problem of post-buckling behavior of long, vertical, circular cylindrical shells loaded by nonuniform pressure, tension, and their own weight is formulated in this paper. The global behavior is considered by assuming that local deformations do not influence the solution. The nonlinear effect is due to the softening of the relationship between the bending moment and curvature due to the effect of the flattening of the shell cross sections. The nonlinear differential equation obtained in this paper describes the post-buckling behavior of a shell with linearly distributed pressure along the axis and arbitrary boundary conditions. In the general case this problem must be solved numerically. An analytical solution is presented for a particular case of a shell loaded by a uniform external or internal pressure.
Nonlinear Six-Degree-of-Freedom Dynamic Model for Risers, Pipelines, and Beams
Authors: Bernitsas Michael M. , Kokarakis John E.
Published: January 2021

A nonlinear model for the dynamic behavior of tubular beams such as marine risers, pipelines, legs of tension leg platforms, and drill strings is developed. The formulation includes three translational degrees of freedom of the riser cross section and three rotational degrees of freedom for shear and torsion. Nonlinear constitutive equations for cross sections of unequal principal stiffnesses and extensible material are derived. Initial structural imperfections which are inherent in long risers are modeled in the form of initial curvature and geometric torsion which do not induce strains. The inertia forces due to the motion of the riser and internal fluid motions are formulated. The external hydrodynamic and hydrostatic forces are integrated on the riser surface as pressure and traction forces. The model is a comprehensive consistent nonlinear formulation of the riser dynamics and can be used for evaluation of the significance of nonlinear effects.
Theory of High-Speed Displacement Ships with Transom Sterns
Authors: Tulin Marshall P. , Hsu C. C.
Published: January 2021

A theory has been developed for high-speed displacement ships with transom sterns; it treats the hull as finite in beam and draft, but slender. The flow is assumed to be smooth at the aft waterline and to have a trailing wake. The trailing wake results in substantial residuary resistance at high speeds for normal waterline ships. This is a completely new finding. Calculations are made for ships of highly variable parametric form and the results are given. This residuary is typically reduced by widening the transom. A shallow draft at the transom is also indicated. A comparison of calculated results with existing experimental data shows good agreement.
Flow Over Tail and in Wake of Axisymmetric Bodies: Review of the State of the Art
Authors: Patel V. C. , Chen H. C.
Published: January 2021

The many methods that have been proposed over the past decade for the calculation of unseparated axisymmetric flow over the tail of a body of revolution are reviewed, and the results of a recently developed method are presented and discussed in detail to assess the state of the art. It is shown that some computational techniques have advanced to a stage where quite accurate solutions can be obtained for such flows.
Ambient Supercavities of Slender Bodies of Revolution
Authors: Vorus William S.
Published: January 2021

Slender-body theory is applied in an analysis of the flow about the general supercavitating streamlined body of revolution. The formulation is specialized to the case of ambient cavity pressure (zero cavitation number) for the specific analysis conducted. Numerical procedures are outlined. The methodology is demonstrated in calculating the cavity shapes, surface velocity distributions, and cavity form drag coefficients for three idealized bodies. These are the convex paraboloid, the conical frustrum, and the concave paraboloid. Characteristic differences in the flows in each of the cases are discussed.
Effects of Waves on the Boundary Layer of a Surface-Piercing Body
Authors: Stern Frederick
Published: January 2021

The boundary-value problem for the boundary layer of a surface-piercing body is formulated in a rigorous manner in which proper consideration is given to the viscous-fluid free-surface boundary conditions. Simplifications that are appropriate for small-amplitude waves are investigated. To this end, order-of-magnitude estimates are derived for the flow field in the neighborhood of the body-boundary-layer/free-surface juncture. It is shown that, for laminar flow, the parameter Ak/ϵ, where Ak is the wave steepness and ϵ is the nondimensional boundary-layer thickness, is important for characterizing the flow. In particular, for Ak/ϵ sufficiently large such that the free-surface boundary conditions have a significant influence a consistent formulation requires the solution of higher-order viscous-flow equations. For turbulent flow, these conclusions cannot be reached with the same degree of certainty. Numerical results are presented for the model problem of a combination Stokes-wave/flat plate. For this initial investigation, the usual thin-boundary-layer equations were solved using a three-dimensional implicit finite-difference method. The calculations are for laminar and turbulent flow and both demonstrate and quantify the influence of waves on boundary-layer development. Calculations were made using both the small-amplitude-wave and more approximate free-surface boundary conditions. Both the external-flow pressure gradients and the free-surface boundary conditions are shown to have a significant influence. The former influence penetrates to a depth of about half the wavelength and the latter is confined to a region very close to the free surface.
On the Hydrodynamics of Tandem-Hull Marine Vehicles
Authors: Patel M. H.
Published: January 2021

The development of ship-shape marine vehicles in naval architecture and semisubmersibles in offshore engineering has proceeded along separate lines with each type of vessel being used for quite different operational needs. A tandem-hull marine vehicle offers a design that bridges the gap in between with a hydrodynamic performance that includes the desirable characteristics of both ships and semisubmersibles for floating oil production applications. A tandem-hull vessel consists of a fully submerged hull positioned a small distance below a surface-piercing hull with interhull bracing connections between the two. However, there are a number of unifying considerations which suggest that all three types of vessels can be regarded as part of a wider family of hull shapes. This paper presents a survey of floating vessel designs to illustrate this point and to highlight the position of a tandem hull as being a design midway between ship and semisubmersible. Leading particulars of the surveyed vessels are manipulated into nondimensional ratios and plotted to show their relationship with each other. The paper also presents a simplified hydrodynamic analysis for heave motion of a tandem hull to highlight the main features underlying its hydrodynamic behavior. The tandem-hull design is also analyzed in detail by a more exact diffraction theory based analysis for wave-induced motions and interhull forces. These predicted motions and forces are compared with data from 1: 75 scale model tests. The analyses and model tests are used to illustrate the principal features that govern hydrodynamic behavior of tandem-hull marine vehicles and that lead to some of their operational advantages as floating oil production vessels.
Numerical Aspects of the Neumann-Kelvin Problem
Authors: Doctors Lawrence J. , Beck Robed F.
Published: January 2021

The Neumann-Kelvin problem for a surface ship traveling at a steady speed represents an approximate solution to the inviscid flow, and is subjected to a range of numerical experiments in the present paper. The solution is obtained by replacing the ship by a surface source distribution. The hull is discretized into a set of flat panels in the numerical procedure. The main difficulty is the accurate calculation of the influence of the various panels on each other. Most previous workers have replaced the wave portion of the potential for each panel by an equivalent source at its centroid (the monopole method) in order to simplify this part of the calculations. In the present work, a technique of analytically integrating the panel source was used, so the above-mentioned approximation was eliminated. A comparison of the two methods shows that the monopole method appears to be less well behaved, in the limit, as the paneling of the hull surface is refined. However, for a course arrangement of panels, the results approximate those, of the consistent-panel technique. Numerical experiments were also performed on a submerged body. In this case, the monopole method is valid, and can be used to advantage to save computing effort.
Shallow-Water Effect on the Motions of Three-Dimensional Bodies in Waves
Authors: Endo Hideichi
Published: January 2021

The motions of three-dimensional bodies of arbitrary shape freely floating in waves in shallow water are studied. The wave loads on and hydrodynamic forces of a rigid body are calculated by applying the surface source distribution method (Green's function method) in the framework of linear wave potential theory. Special attention is paid to the numerical evaluation of the Green function for finite water depth; namely, an improper integral containing a singularity in the Green function is obtained by Gauss-Laguerre quadrature, and the ∫1 lr* ds term obtained is by numerical quadrature. Computational results of wave exciting forces, hydrodynamic coefficients, and motions of freely floating structures in shallow and deep water are compared with those obtained in the literature. Furthermore, the shallow-water effect on the motions of a large structure is examined.
Potential of Optimal Ship Structure Redesign for Minor Collisions
Authors: Robeson D. E. , Haftka R. T. , Sundkvist K. E.
Published: January 2021

An optimization technique is used to investigate changes in structural design which will increase the energy-absorbing capabilities of a marine vessel during a low-speed collision. The idealized collision scenario is arigid, vertical bow striking a tanker at a right angle, midway between rigid bulkheads. Collision energy is most efficiently absorbed as membrane tension. A penalty function method is utilized to redesign a compartment of a large tanker for rupture resistance. Up to 130 percent increase of energy absorbed prior to rupture is obtained for optimal designs without increase in weight but with sacrifice of strength. Stronger, more conservative designs are investigated by restraining the parametric freedom. Trends for improving rupture resistance are presented.
Reliability-Based Design Format for Marine Structures
Authors: White Gregory J. , Ayyub Bilal M.
Published: January 2021

Recently there has been increased effort by classification societies and design authorities to bring reliability analysis into the design process. Typically these efforts involve using some reliability analysis method to calculate "partial safety factors" for design equations. The mean-value first-order second-moment method (MVFOSM), the advanced second-moment method (ASM), and an "exact" method have been used, or are being proposed for use, in the design of marine structures. In some recent work it has been shown that design formats based on the first two methods may result in engineering designs of different reliability levels than the ones specified in developing the design formats. These three methods are evaluated and a "reliability-conditioned (RC) method" is proposed in this paper. The proposed method overcomes the shortcomings of the MVFOSM and ASM methods and extends the concepts of the "exact" method in a more useful form to handle general types of problems. The RC method is believed to result in partial safety factors which give engineering designs of reliability levels equal to the specified ones.
The Hydrodynamics of Water on Deck
Authors: Jones Alan F. , Hulme A.
Published: January 2021

We consider the wave motion produced in a rolling water-filled tank, which models the hydrodynamics of water trapped on a ship's deck. The waves produced are seen to depend on the values of four dimensionless parameters. Discussion is given of the most physically relevant of the many possible parameter regimes. Solutions are found by a combination of asymptotic and numerical methods. It is shown that significant turning moments can be exerted on the vessel by the transient waves that are produced in the general case. Even larger effects are possible if the forcing frequency happens to lie close to a resonance frequency of the system.
Design of Dome Ends to Withstand Uniform External Pressure
Authors: Ross C. T. F.
Published: January 2021

A radical proposal is suggested for a more efficient design of dome ends to withstand uniform external pressure. A qualitative design of a cylinder/dome combination is considered, together with a stress investigation, using the finite-element method. These have shown that this design is feasible.
Evaluation of the Wave-Resistance Green Function: Part 1—The Double Integral
Authors: Newman J. N.
Published: January 2021

Analytical and numerical studies are made of the source potential for steady motion beneath a free surface. Various alternative integral representations are reviewed, and attention is focused on the component which usually is expressed as a double integral. A particular form is selected for numerical applications, where the double integral represents a symmetrical nonradiating disturbance, and the far-field waves are accounted for separately in the complementary single integral. Systematic expansions are derived for the singularity of the double integral at the origin, and for its asymptotic behavior far from the origin. Guided by these expansions, numerical approximations of the double integral are derived in terms of three-dimensional polynomials, which greatly facilitate the computation of the double integral. Tables of the coefficients in these approximations are presented, permitting the double integral to be evaluated throughout the three-dimensional domain with an accuracy of five to six decimal places. Greater accuracy can be achieved by using extended tables of the same coefficients. Algorithms for evaluating the Chebyshev polynomial approximations and a description of the computational methods used to derive the coefficients are included in the Appendices.
Evaluation of the Wave-Resistance Green Function: Part 2—The Single Integral on the Centerplane
Authors: Newman J. N.
Published: January 2021

Effective series expansions are derived for the evaluation of the single integral in the potential of a submerged source which moves with constant velocity, when the source and field point are in the same longitudinal centerplane. In conjunction with the polynomial approximations for the double integral component which have been derived in Part 1 of this work, the present results facilitate the computation of the source potential or Green function. Three complementary domains of the centerplane are considered, with different expansions developed for use in each domain. The principal expansion is based on a Neumann series which is effective for small or moderate distances from the origin, except in a thin region near the free surface. To deal with the latter domain an asymptotic expansion is derived in ascending powers of the vertical coordinate. Both of these expansions are refined by subtracting a simpler component with the same behavior at the origin, and relating this component to Dawson's integral. Special algorithms for the evaluation of the latter function are presented in the Appendix. The third and final expansion, based upon the method of steepest descents, is effective at large distances from the origin. This asymptotic series is derived by a systematic recursive scheme to permit an arbitrary order of the approximation. Used in conjunction with the first two expansions, this permits the single integral to be evaluated with an absolute accuracy of six decimals throughout the centerplane.
A Novel Submarine Pressure Hull Design
Authors: Ross C. T. F.
Published: January 2021

The paper presents an alternative design for a submarine pressure hull, which has no ring-stiffeners, but where shell instability and general instability are resisted by making the pressure hull of a swedged-shaped form. Calculations on two different-sized pressure hulls appear to indicate that the swedged-shaped hulls are more structurally efficient than their ring-stiffened equivalents.
Mixing Lengths or Eddy Viscosities for Thick Axisymmetric Turbulent Boundary Layers Near a Wall
Authors: Granville Paul S.
Published: January 2021

A mixing-length formulation is proposed for thick axisymmetric turbulent boundary layers near a wall; it is based on the classical similarity-law analysis. Comparison is made with existing formulations.
Convergence Properties of the Neumann-Kelvin Problem for a Submerged Body
Authors: Doctors Lawrence J. , Beck Robert F.
Published: January 2021

The Neumann-Kelvin method for solving the flow past a body moving at a steady speed requires that the body boundary condition be satisfied exactly, while the free-surface condition is satisfied in a linearized sense. The solution is generally obtained by discretizing the body surface into panels, each of which has an unknown singularity strength. In the present work, two types of numerical experiments have been carried out. In the first approach, the body condition is satisfied at one point on each panel (the collocation method). In the second approach, the body condition is satisfied in an integrated sense on each panel (the Galerkin method). Improved convergence properties are demonstrated by the second approach.
A Study of Plate Tearing for Ship Collision and Grounding Damage
Authors: Jones Norman , Jouri W. S.
Published: January 2021

Some experimental test results are presented herein for the cutting of steel plates which are struck on one edge by a rigid wedge. These results were obtained on thicker plates than examined previously and are consistent with the earlier test data that were reported on the thinner plates. Empirical formulas are developed for the cutting, bending and friction energies absorbed in the steel plates and appear to provide reasonable agreement with the corresponding test results. A few preliminary test results are also reported for rigid wedges having rounded tips. The results of this study support earlier suggestions that, when plate tearing and cutting occurs, the damage of full-scale prototypes is greater than that expected from the behavior of small-scale models using the elementary principles of geometrically similar scaling.
A Method for Calculating the Michell and Havelock Integrals
Authors: de Sendagorta M. , Grases J.
Published: January 2021

A method is suggested for analyzing and calculating the Michell and Havelock integrals. In place of the corresponding integral expressions, infinite series are proposed that do not require many terms for accuracy. Shape dependence is presented by way of products of integral functions that define the ship. It is thus possible to analyze the effect of shape variation by varying these functions without integrating them. Velocity dependence is linear with respect to integral functions that are shape-independent and hence suitable for tabulation. Values afforded by the Michell and Havelock integrals are to an extent tied to wave resistance. It is believed that to the same extent the method proposed herein is especially apt for (i) the systematic analysis of ship series and (ii) computer-aided shape design.
Nonlinear Analysis of Geometrically Imperfect Stiffened Shells of Revolution
Authors: Subbiah J.
Published: January 2021

A nonlinear, large-deformation, finite-element formulation is presented for the analysis of general instability of ring-stiffened shells of revolution subjected to combined end compression and circumferential pressure loading. The pressure loading is treated as a follower force. The effect of varying degrees of initial imperfection on the load displacement behavior is reported. A combined nonlinear and eigenvalue analysis is presented to determine critical pressures for initially imperfect, stiffened cylinders.
A Note on the Secondary Vortex Caused by a Thin Foil in a Nonuniform Flow
Authors: Yim B.
Published: January 2021

WHEN A finite span lifting wing is located in a uniform flow, trailing vortices are generated by the wing. It is well known from the Kelvin theorem that the trailing vortex strength is proportional to the spanwise slope of the bound vortex distribution. When the wing is located in a nonuniform flow, the problem becomes complex. Such flow has been dealt with by Vandry [1], 2 Karman and Tshen [2], Honda [8], and Smith [4]. It has been found that this flow has an extra trailing vortex created by the interaction between the nonuniform flow and the wing. This extra vortex is called the secondary vortex and has been studied extensively in connection with the theory of turbomachinery.
A Two-Dimensional Potential Flow Model of the Wave Field Generated by a Semisubmerged Body in Heaving Motion
Authors: Wang X. M. , Spaulding M. L.
Published: January 2021

A two-dimensional potential flow model is formulated to predict the wave field and forces generated by a sere!submerged body in forced heaving motion. The potential flow problem is solved on a boundary fitted coordinate system that deforms in response to the motion of the free surface and the heaving body. The full nonlinear kinematic and dynamic boundary conditions are used at the free surface. The governing equations and associated boundary conditions are solved by a second-order finite-difference technique based on the modified Euler method for the time domain and a successive overrelaxation (SOR) procedure for the spatial domain. A series of sensitivity studies of grid size and resolution, time step, free surface and body grid redistribution schemes, convergence criteria, and free surface body boundary condition specification was performed to investigate the computational characteristics of the model. The model was applied to predict the forces generated by the forced oscillation of a U-shaped cylinder. Numerical model predictions are generally in good agreement with the available second-order theories for the first-order pressure and force coefficients, but clearly show that the third-order terms are larger than the second-order terms when nonlinearity becomes important in the dimensionless frequency range 1≤ Fr≤ 2. The model results are in good agreement with the available experimental data and confirm the importance of the third order terms.
On the Undesirable Roll Characteristics of Ships in Regular Seas
Authors: Nayfeh All H.
Published: January 2021

In 1863 Froude observed that a ship whose frequency in pitch (heave) is twice its frequency in roll has undesirable roll characteristics. To explain this phenomenon, Paulling and Rosenberg as well as Kinney assumed the pitch (heave) motion to be a simple harmonic independent of the roll motion. Substituting the pitch (heave) expression into the roll equation, they obtained a Mathieu equation. They found that exponentially growing instabilities can occur for certain pitch amplitudes and frequency ratios. The exponential growth is unrealistic, the result of their neglecting the influence of the roll motion on the pitch (heave) motion. To improve their results, the present author offers an analysis for the nonlinear coupling of the pitch and roll modes of ship motions in regular seas. When the encounter frequency is near the pitch frequency, only the pitch mode is excited if the encountered wave amplitude (excitation amplitude) is small. As the excitation amplitude increases, the amplitude of the pitch mode increases in accordance with linear theory until it reaches a critical small value. As the excitation amplitude increases further, the pitch amplitude does not change from the critical value (that is, the pitch mode is saturated), and all the extra energy is transferred to the roll mode. Consequently, for large excitation amplitudes, the response is a combined roll and pitch motion, with the amplitude of the roll mode being very much larger than that of the pitch mode. More dangerously, the nonlinear theory predicts instabilities in regions where the linear theory predicts stability. Moreover, the nonlinear theory predicts conditions for the nonexistence of steady-state periodic responses. Instead, the responses can be amplitude- and phase-modulated roll and pitch motions or even chaotic. When the encounter frequency is near the roll frequency, there is no saturation phenomenon and, at close to perfect resonance, there are no steady-state periodic responses in some cases. The present results indicate that large roll amplitudes are likely in this case also. Further, the results predict the possibility of large amplitudes in the roll motion even when the ship is moving through a head or following sea.
Bubble Dynamics and Cavitation Inception Theory
Authors: Parkin Blaine R. , Baker Brian B.
Published: January 2021

In order to provide some theoretical background and to motivate the more refined theory introduced herein, some encouraging known theoretical results on bubble-ring cavitation inception are reviewed. This review is followed by the development of the theory of bubble-ring cavitation cutoff. Its outcome, when compared with experiment, shows the need for a more refined inception theory. The above comparison and the basic ideas behind the cutoff theory's formulation suggest a possible approach for a refinement based on a multiple scales expansion. This seems reasonable because the forcing function pulse in "laboratory time" f, varies slowly compared with the characteristic "bubble time,", which characterizes the response time of a typical microscopic cavitation nucleus. The ratio of these two times gives a small parameter, , appearing in the forcing function, with the result that this problem involves only a soft excitation. Expanding the forced Rayleigh-Plesset equation and its initial conditions to the second order in c, the zeroth-order problem is found to be the well-known autonomous nonlinear equation with nonhomogeneous initial conditions, giving free oscillations of a typical nucleus. The first-order system is a nonautonomous linear system with homogeneous initial conditions which governs the forced bubble growth. The second-order system consists of a linear autonomous differential equation and homogeneous initial conditions. It is needed to establish integrability conditions for the first-order solution. The first-order solution is left for future research and the zeroth-order problem is analyzed in the phase plane. Then a novel approximate integration, = t(u), is given in terms of elliptic integrals and functions. It was not possible to invert this solution and so the inverse u = u() is found numerically. These data are then used to find an analytical approximation for use in future first-order calculations.
Rigid-Plastic Response of Floating Plates
Authors: Anastasiadis John , Xirouchakis Paul C.
Published: January 2021

This paper presents the exact formulation and solution for the static flexural response of a rigid perfectly plastic freely floating plate subjected to lateral axisymmetric loading. The Tresca yield condition is adopted with the associated flow rule. The plate response is divided into three phases: Initially the plate moves downward into the foundation as a rigid body (Phase I). Subsequently the plate deforms in a conical mode in addition to the rigid body motion (Phase II). At a certain value of the load a hinge-circle forms which may move as the pressure increases further (Phase III). The nature of the solution during the third phase depends upon the parameter α = a/R (ratio of radius of loaded area to the plate radius). When α = αs≅ 0.46 the hinge-circle remains stationary under increasing load. For α < αs the hinge-circle shrinks, whereas for α > αs the hinge-circle expands with increasing pressure. The application of the present results to the problem of laterally loaded floating ice plates is discussed.
Side Forces on a Ship’s Hull
Authors: Hunter W. S. , Joubert P. N.
Published: January 2021

Side forces on a ship traveling at small yaw angles are predicted using slender-body theory. The approach uses the method of matched asymptotic expansions, with a cascade of flat plates as a model for the submarine portion of the ship's hull. Resulting predictions of side force coefficients are then compared with experimentally measured values derived from towing tank tests of a typical (tanker) hull. Correlation between theoretical and experimental results was very good for yaw angles less than 8 deg at low Froude number (Fn = 0.134).
Eddy Viscosities and Mixing Lengths for Turbulent Boundary Layers on Flat Plates, Smooth or Rough
Authors: Granville Paul S.
Published: January 2021

Algebraic formulas are derived here for the eddy viscosities and mixing lengths of turbulent boundary layers on flat plates. The effect of low Reynolds numbers, especially on rough surfaces, is included. The formulas are based on the similarity laws and the equations of motion. Both smooth and rough surfaces are considered. The agreement with Klebanoff's measurements is excellent.
A Viscous-Flow Approach to the Computation of Propeller-Hull Interaction
Authors: Stern F. , Kim H. T. , Patel V. C. , Chen H. C.
Published: January 2021

A model is developed to simulate two-dimensional laminar flow over an arbitrarily shaped body, a part of which is subjected to simple harmonic motion. The vibration amplitude ratio, Ho, and the Reynolds number, Re, are maintained at 0.1 and 1000, respectively. The Strouhal number, St, is varied in the range 0.0 ≤ St ≤ 1.0. The computer code is tested for the flow in a square cavity and also over a flat plate. The friction and pressure coefficients over the vibrating portion of the body are determined. Fast Fourier Transforms are performed on the time series data of these coefficients. For low-frequency vibrations (low Strouhal number) the pressure and friction coefficients match the steady-state results for flow over a sinusoidal bump. A small-amplitude pressure wave generated by the oscillating plate propagates downstream with the flow. For high-frequency vibrations (high Strouhal number) the pressure and friction coefficients over the vibrating portion of the body deviate from the steady-state results and a high-amplitude pressure wave propagates downstream. The pressure at one chord length upstream is also affected. As St increases, the flow becomes highly nonlinear and higher harmonics appear in the downstream flow. Subsequent analysis indicates that the nonlinearity is controlled by the term v(Əu/Əy).
Generalization of Taylor’s Added-Mass Formula for Two Bodies
Authors: Landweber L. , Chwang A. T.
Published: January 2021

A previous generalization of the Taylor formula, which expresses the added masses of a single body, moving with six degrees of freedom, in terms of the system of hydrodynamic singularities which generate the irrotational flow about the body, is further generalized for the case when another moving body is present. This work was stimulated by a study of the hydrodynamic interactions between an ice mass and a ground-based offshore structure. The results are applied to calculate the variation of the added masses as a rectangular cylinder approaches a circular one. A new simple relation between the added masses of a rectangle moving parallel to its longer or shorter side, and a more complete table of the added-mass coefficients for various thickness-length ratios than was previously available, is presented in the Appendix.
Near and Far-Field Evaluations of the Free-Surface Multipole Potential
Authors: Cohen Stuart B.
Published: January 2021

The general mth-order, free-surface, multipole velocity potential is considered and found suitable for arrays of spherical devices requiring interactions between the devices. Expansions into an infinite series representation and an integral representation with finite limits are shown. These expressions can be evaluated by digital computer to any degree of accuracy and are formulated for especially rapid evaluation in certain regions: the series representation for small field distances, and the integral representation for large distances. Tables of the potentials and their Cartesian and radial derivatives are given to eight significant figures. Illustrations of multipoles between m = 0 and m = 4 are shown.
The Effects of Energy Dissipation on the Transition to Planing of a Boat
Authors: Naghdi P. M. , Rubin M. B.
Published: January 2021

The problem of the transition to planing of a boat, in the presence of the effect of spray formation at the boat's leading edge, is investigated using a nonlinear steady-state solution of the equations of the theory of a directed fluid sheet for two-dimensional motion of an incompressible inviscid fluid. The motion of the fluid is coupled with the motion of the free-floating boat and detailed analysis is undertaken pertaining to such features as trim angle, sinkage, and propulsion force. The effects of the rate of energy dissipation arising from spray formation at the boat's leading edge, and changes in equilibrium depth, propulsion angle, and the boat's weight, are studied and shown to significantly influence the boat's planing characteristics.
Hydrodynamic Analysis of the Sweeping of a "Ro"—an Oriental Scull
Authors: Azuma Akira , Furuta Toyohiko , luchi Matsusaburo , Watanabe Isao
Published: January 2021

The "ro" and "kai" are kinds of oriental sculls used to propel and to steer small boats and have been utilized for a long time in Japan. Analytic and experimental studies are performed to understand the mechanisms of locomotion of the ro and kai. Simple momentum theory and the local circulation method, together with the blade element theory, are applied to obtain the hydrodynamic characteristics of the ro and these are compared with experimental test data. The results show that the matching of the ro with the hull is excellent in the hydrodynamic sense and that the operation of the ro is also conducted with optimal efficiency.