The Damping and Wave Resistance of a Pitching and Heaving Ship

1959 ◽  
Vol 3 (02) ◽  
pp. 1-19 ◽  
Author(s):  
J. N. Newman
Keyword(s):  
Velocity Potential ◽  
Oscillation Amplitude ◽  
Cross Coupling ◽  
Wave Resistance ◽  
Beam Length ◽  
Damping Coefficients ◽  
Calm Water ◽  
Polynomial Hull ◽  
Perturbation Parameters ◽  
Energy Components

This paper considers the damping and wave resistance of a thin ship which is moving in calm water with constant velocity and oscillating in pitch and heave. The velocity potential is obtained from Green's theorem after a process of systematic linearization in terms of perturbation parameters representing the beam-length ratio and the oscillation amplitude. An asymptotic expansion of the Green's function is derived from which the energy radiation is obtained. The coefficients of damping and increased wave resistance are then found by separation of the energy components. No separation of the two cross-coupling damping coefficients is obtained, however. Calculations are presented for a polynomial hull and compared with experimental data.

scholarly journals Surge motion on a floating cylinder in water of finite depth

2003 ◽  
Vol 2003 (57) ◽  
pp. 3643-3656 ◽  
Author(s):  
Dambaru D. Bhatta
Keyword(s):  
Velocity Potential ◽  
Separation Of Variables ◽  
Finite Depth ◽  
Added Mass ◽  
Computational Results ◽  
Complex Matrix ◽  
Interior Region ◽  
Exterior Region ◽  
Damping Coefficients ◽  
Calm Water

We derived added mass and damping coefficients of a vertical floating circular cylinder due to surge motion in calm water of finite depth. This is done by deriving the velocity potential for the cylinder by considering two regions, namely, interior region and exterior region. The velocity potentials for these two regions are obtained by the method of separation of variables. The continuity of the solutions has been maintained at the imaginary interface of these regions by matching the functions and gradients of each solution. The complex matrix equation is numerically solved to determine the unknown coefficients. Some computational results are presented for different depth-to-radius and draft-to-radius ratios.

scholarly journals Hydrodynamic Forces Exerting on an Oscillating Cylinder under Translational Motion in Water Covered by Compressed Ice

Water ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 822
Author(s):  
Yury Stepanyants ◽  
Izolda Sturova
Keyword(s):  
Lift Force ◽  
Wave Motion ◽  
Translational Motion ◽  
Added Mass ◽  
Hydrodynamic Forces ◽  
Wave Resistance ◽  
Translational Velocity ◽  
Damping Coefficients ◽  
Incompressible Ideal Fluid ◽  
Theoretical Results

This paper presents the calculation of the hydrodynamic forces exerted on an oscillating circular cylinder when it moves perpendicular to its axis in infinitely deep water covered by compressed ice. The cylinder can oscillate both horizontally and vertically in the course of its translational motion. In the linear approximation, a solution is found for the steady wave motion generated by the cylinder within the hydrodynamic set of equations for the incompressible ideal fluid. It is shown that, depending on the rate of ice compression, both normal and anomalous dispersion can occur in the system. In the latter case, the group velocity can be opposite to the phase velocity in a certain range of wavenumbers. The dependences of the hydrodynamic loads exerted on the cylinder (the added mass, damping coefficients, wave resistance and lift force) on the translational velocity and frequency of oscillation were studied. It was shown that there is a possibility of the appearance of negative values for the damping coefficients at the relatively big cylinder velocity; then, the wave resistance decreases with the increase in cylinder velocity. The theoretical results were underpinned by the numerical calculations for the real parameters of ice and cylinder motion.

On the Radiation and Diffraction of Surface Waves by Submerged Spheroids

1989 ◽  
Vol 33 (02) ◽  
pp. 84-92
Author(s):  
G. X. Wu ◽  
R. Eatock Taylor
Keyword(s):  
Degrees Of Freedom ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Added Mass ◽  
Wave Radiation ◽  
Legendre Functions ◽  
Incoming Wave ◽  
Six Degrees Of Freedom ◽  
Damping Coefficients ◽  
Exciting Forces

The problem of wave radiation and diffraction by submerged spheroids is analyzed using linearized three-dimensional potential-flow theory. The solution is obtained by expanding the velocity potential into a series of Legendre functions in a spheroidal coordinate system. Tabulated and graphical results are provided for added mass and damping coefficients of various spheroids undergoing motions in six degrees of freedom. Graphs are also provided for exciting forces and moments corresponding to a range of incoming wave angles.

An Analysis of Heave Added Mass and Damping of a Surface-Effect Ship

1981 ◽  
Vol 25 (01) ◽  
pp. 44-61
Author(s):  
C. H. Kim ◽  
S. Tsakonas
Keyword(s):  
Free Surface ◽  
High Speed ◽  
Surface Effect ◽  
Practical Method ◽  
Added Mass ◽  
Damping Coefficients ◽  
Calm Water ◽  
Surface Effect Ship ◽  
Long Time ◽  
Computational Procedures

The analysis presents a practical method for evaluating the added-mass and damping coefficients of a heaving surface-effect ship in uniform translation. The theoretical added-mass and damping coefficients and the heave response show fair agreement with the corresponding experimental values. Comparisons of the coupled aero-hydrodynamic and uncoupled analytical results with the experimental data prove that the uncoupled theory, dominant for a long time, that neglects the free-surface effects is an oversimplified procedure. The analysis also provides means of estimating the wave elevation of the free surface, the escape area at the stern and the volume which are induced by a heaving surface-effect ship in uniform translation in otherwise calm water. Computational procedures have been programmed in the FORTRAN IV language and adapted to the PDP-10 high-speed digital computer.

Experimental Investigation of Hydrodynamic Coefficients of a Wave-Piercing Tumblehome Hull Form

2007 ◽  
Author(s):  
Christopher C. Bassler ◽  
Jason B. Carneal ◽  
Paisan Atsavapranee
Keyword(s):  
Experimental Investigation ◽  
System Modeling ◽  
Flow Simulation ◽  
Roll Damping ◽  
Hull Form ◽  
Damping Coefficients ◽  
Calm Water ◽  
Forced Roll ◽  
Future Work ◽  
Damping Model

A systematic series of calm-water forced roll model tests were performed over a range of forward speeds using an advanced tumblehome hull form (DTMB model #5613-1) to examine the mechanisms of roll damping. This experimental investigation is part of an ongoing effort to advance the capability to assess seakeeping, maneuvering, and dynamic stability characteristics of an advanced surface combatant. The experiment was performed to provide data for development and validation of a semi-empirical roll damping model for use in validation of ship motion and viscous flow simulation codes, as well as to provide a basis for future work with additional experiments, contributing to the development of an improved analytical roll damping model. Two hull configurations were tested: barehull with skeg, and bare hull with skeg and bilge keels. Measurements of forces and moments were obtained over a range of forward speeds, roll frequencies, and roll amplitudes. Stereo particle-image velocimetry (SPIV) measurments were also taken for both zero and forward speeds. Test data was used to calculate added mass/inertia and damping coefficients. Two different system modeling techniques were used. The first method modeled the system as an equivalent linearly-damped second-order harmonic oscillator with the time-varying total stiffness coefficient considered linear. The second technique used equivalent linear damping, including higher-order Fourier components, and a non-linear stiffness formulation. Results are shown, including plots of added inertia and damping coefficients as functions of roll frequency, roll amplitude, and forward speed and SPIV measurements. Trends from the experimental data are compared to results from traditional component roll damping formulations for conventional hull from geometries and differences are discussed.

Stability of Rotor-Bearing Systems With Generalized Support Flexibility and Damping and Aerodynamic Cross-Coupling

1975 ◽  
Vol 97 (3) ◽  
pp. 461-469 ◽  
Author(s):  
R. E. Warner ◽  
A. I. Soler
Keyword(s):  
Cross Coupling ◽  
Frequency Dependent ◽  
Oil Film ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Single Mass ◽  
Tilting Pad Bearings

This paper examines stability of the flexible single mass rotor, acted on by motion induced forces due to aero-dynamic cross-coupling and supported most generally by oil film tilting pad bearings which are in turn mounted on flexible, damped supports. Plotted results include the frequency dependent spring and damping coefficients for the 4-pad tilting pad bearing, damping coefficients for the 360-deg squeeze bearing and stability plots of rotor-bearing systems including aerodynamic cross-coupling, the 4-pad tilting pad bearing and the 150-deg partial arc bearing with various support arrangements.

Convergence of a Sequence of Slender-Ship Low-Froude-Number Wave-Resistance Approximations

1984 ◽  
Vol 28 (03) ◽  
pp. 155-162
Author(s):  
Francis Noblesse
Keyword(s):  
Froude Number ◽  
Wave Resistance ◽  
Beam Length ◽  
Remarkable Property ◽  
Ship Hulls ◽  
Low Froude Number ◽  
Vertical Cylinders ◽  
Elliptical Cylinders ◽  
Double Hull ◽  
Special Case

Convergence of the sequence of slender-ship low-Froude-number wave-resistance approximations /"/, n > 0, obtained as a particular case of the slender-ship theory of wave resistance recently proposed by the author, is proved for the special case of ship hulls in the form of vertical cylinders with elliptical waterlines. Specifically, it is shown that we have where b is the thickness (beam/length) ratio of the cubical cylinder, Fis the Froude number, and r lf(b,F) is the Guevel-Baba-Maruo-Kayo low-Froude-number wave-resistance approximation associated with the exact zero-Froude-number (double-hull) potential. Vertical elliptical cylinders thus have the remarkable property that the ratio iipj{b,F)/rpp(b,F) is independent of the Froude number, that is, depends only on the thickness ratio of the cylinder.

Radiation and diffraction of water waves by a submerged sphere at forward speed

1988 ◽  
Vol 417 (1853) ◽  
pp. 433-461 ◽  
Keyword(s):  
Water Waves ◽  
Velocity Potential ◽  
Surface Condition ◽  
Wave Resistance ◽  
The Body ◽  
Legendre Functions ◽  
Forward Speed ◽  
Submerged Sphere ◽  
Exciting Forces ◽  
Similar Equation

A submerged sphere advancing in regular deep-water waves at constant forward speed is analysed by linearized potential theory. A distribution of sources over the surface of the sphere is expanded into a series of Legendre functions, by extension of the method used by Farell ( J . Ship Res . 17, 1 (1973)) in analysing the wave resistance on a submerged spheroid. The equations governing the velocity potential are satisfied by use of the appropriate Green function and by choosing the coefficients in the series of Legendre functions such that the body surface condition is satisfied. Numerical results are obtained for the wave resistance, hydrodynamic coefficients and exciting forces on the sphere. Some theoretical aspects of a body advancing in waves are also discussed. The far-field equation of Newman ( J . Ship Res . 5, 44 (1961)) for calculation of the damping coefficients is extended, and a similar equation for the exciting forces is derived.

scholarly journals Global relationships between two-dimensional water wave potentials

1996 ◽  
Vol 312 ◽  
pp. 299-309 ◽  
Author(s):  
M. McIver
Keyword(s):  
Water Wave ◽  
Small Amplitude ◽  
Velocity Potential ◽  
Two Dimensional ◽  
Reciprocity Relations ◽  
Moving Body ◽  
Calm Water ◽  
Exciting Forces ◽  
Scattering Potential ◽  
Scattering And Radiation

When a body interacts with small-amplitude surface waves in an ideal fluid, the resulting velocity potential may be split into a part due to the scattering of waves by the fixed body and a part due to the radiation of waves by the moving body into otherwise calm water. A formula is derived which expresses the two-dimensional scattering potential in terms of the heave and sway radiation potentials at all points in the fluid. This result generalizes known reciprocity relations which express quantities such as the exciting forces in terms of the amplitudes of the radiated waves. To illustrate the use of this formula beyond the reciprocity relations, equations are derived which relate higher-order scattering and radiation forces. In addition, an expression for the scattering potential due to a wave incident from one infinity in terms of the scattering potential due to a wave from the other infinity is obtained.

scholarly journals Wave loadings on a vertical cylinder due to heave motion

1995 ◽  
Vol 18 (1) ◽  
pp. 151-170 ◽  
Author(s):  
D. D. Bhatta ◽  
M. Rahman
Keyword(s):  
Velocity Potential ◽  
Diffraction Problem ◽  
Vertical Cylinder ◽  
Finite Depth ◽  
Wave Forces ◽  
Wave Loads ◽  
Exterior Region ◽  
Calm Water ◽  
Heave Motion ◽  
Fixed Structure

Wave forces and moments due to scattering and radiation for a vertical circular cylinder heaving in water of finite depth are derived analytically. These are derived from the total velocity potential which can be decomposed as two velocity potentials; one due to scattering in the presence of an incident wave on fixed structure (diffraction problem), and the other due to radiation by the heave motion on calm water (radiation problem). For each part, the velocity potential is derived by considering two regions, namely, interior region and exterior region. The complex matrix equations are solved numerically to determine the unknown coefficients to compute the wave loads. Some numerical results are presented for different depth to radius and draft to radius ratios.

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