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 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.

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.

On the Drift Forces of a Vertical Cylinder in Water of Finite Depth

2004 ◽  
Author(s):  
Matiur Rahman ◽  
S. Hossein Mousavizadegan
Keyword(s):  
Analytical Solutions ◽  
Gaussian Quadrature ◽  
Vertical Cylinder ◽  
Finite Depth ◽  
Interior Region ◽  
Exterior Region ◽  
Gaussian Quadrature Formula ◽  
Analytical Technique ◽  
Wave Induced ◽  
Drift Forces

Analytical solutions for the wave-induced second-order time independent drift forces and moments due to the dynamic and the waterline pressures on a fixed vertical circular cylinder are derived. The results are displayed graphically for a number of depth to radius ratios. An analytical technique is used to determine the first-order velocity potential by considering two regions, namely, interior region and exterior region. We have also demonstrated a numerical solution by a higher order panel method in which the kernel of the integral equation is modified to make it non-singular and amenable to solutions by the Gaussian quadrature formula. The numerical results are found to comply with the analytical solutions.

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 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.

Measured Static and Rotordynamic Coefficient Results for a Rocker-Pivot, Tilting-Pad Bearing With 50 and 60% Offsets

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Chris D. Kulhanek ◽  
Dara W. Childs
Keyword(s):  
Dynamic Stiffness ◽  
Mass Matrix ◽  
Excitation Frequency ◽  
Quadratic Function ◽  
Added Mass ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Tilting Pad ◽  
Frequency Independent ◽  
Direct Stiffness

Static and rotordynamic coefficients are measured for a rocker-pivot, tilting-pad journal bearing (TPJB) with 50 and 60% offset pads in a load-between-pad (LBP) configuration. The bearing uses leading-edge-groove direct lubrication and has the following characteristics: 5-pads, 101.6 mm (4.0 in) nominal diameter,0.0814 -0.0837 mm (0.0032–0.0033 in) radial bearing clearance, 0.25 to 0.27 preload, and 60.325 mm (2.375 in) axial pad length. Tests were performed on a floating bearing test rig with unit loads from 0 to 3101 kPa (450 psi) and speeds from 7 to 16 krpm. Dynamic tests were conducted over a range of frequencies (20 to 320 Hz) to obtain complex dynamic stiffness coefficients as functions of excitation frequency. For most test conditions, the real dynamic stiffness functions were well fitted with a quadratic function with respect to frequency. This curve fit allowed for the stiffness frequency dependency to be captured by including an added mass matrix [M] to a conventional [K][C] model, yielding a frequency independent [K][C][M] model. The imaginary dynamic stiffness coefficients increased linearly with frequency, producing frequency-independent direct damping coefficients. Direct stiffness coefficients were larger for the 60% offset bearing at light unit loads. At high loads, the 50% offset configuration had a larger stiffness in the loaded direction, while the unloaded direct stiffness was approximately the same for both pivot offsets. Cross-coupled stiffness coefficients were positive and significantly smaller than direct stiffness coefficients. Negative direct added-mass coefficients were obtained for both offsets, especially in the unloaded direction. Cross-coupled added-mass coefficients are generally positive and of the same sign. Direct damping coefficients were mostly independent of load and speed, showing no appreciable difference between pivot offsets. Cross-coupled damping coefficients had the same sign and were much smaller than direct coefficients. Measured static eccentricities suggested cross coupling stiffness exists for both pivot offsets, agreeing with dynamic measurements. Static stiffness measurements showed good agreement with the loaded, direct dynamic stiffness coefficients.

Ship Motions in Shallow Water

1970 ◽  
Vol 14 (04) ◽  
pp. 317-328 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Incident Wave ◽  
Degrees Of Freedom ◽  
Added Mass ◽  
Exciting Force ◽  
Ship Motions ◽  
Wave System ◽  
Six Degrees Of Freedom ◽  
Damping Coefficients

The problem discussed concerns small motions of a ship, in all six degrees of freedom, but at zero speed of advance, due to an incident wave system in shallow water of depth comparable with the ship's draft. The problem is completely formulated for an arbitrary ship, and is partially solved for the case when the ship is slender and the wavelength much greater than the water depth. Sample numerical computations of heave, pitch, and sway added mass and damping coefficients and the sway exciting force are presented.

The Disturbance Due to a Slender Ship Oscillating in Waves in a Fluid of Finite Depth

1966 ◽  
Vol 10 (04) ◽  
pp. 242-252 ◽  
Author(s):  
V. J. Monacella
Keyword(s):  
Ideal Fluid ◽  
Asymptotic Approximation ◽  
Velocity Potential ◽  
Wave Length ◽  
Hydrodynamic Pressure ◽  
Finite Depth ◽  
First Order ◽  
Incident Plane ◽  
Progressive Waves ◽  
Body Potential

The disturbance due to a ship, free to oscillate on the surface of an ideal fluid of finite depth, is studied. The ship is in the presence of oblique, incident, plane progressive waves. Green's theorem is used to represent the velocity potential, and an asymptotic approximation for the first-order slender-body potential valid for all points in the fluid to within a wave length of the ship is found. This is used to determine the hydrodynamic pressure on the bottom of the fluid. Numerical results are presented for the case of a spheroid.

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