scholarly journals Modeling of Coupled Roll and Yaw Damping of a Floating Body in Waves

2007 ◽  
Vol 2007 ◽  
pp. 1-17 ◽  
Author(s):  
S. K. Das ◽  
S. N. Das
Keyword(s):  
Perturbation Technique ◽  
Mathematical Formulation ◽  
Closed Form Solution ◽  
Added Mass ◽  
Form Solution ◽  
Floating Body ◽  
Step Size ◽  
Weakly Nonlinear ◽  
Mass Moment ◽  
Small Distortion

A mathematical model is described to investigate the damping moment of weakly nonlinear roll and yaw motions of a floating body in time domain under the action of sinusoidal waves. The mathematical formulation for added mass moment of inertia and damping is presented by approximating time-dependent coefficients and forcing moments when small distortion holds. Using perturbation technique, we obtain orderwise equations wherein the closed-form solution is obtained for zeroth-order case, and for higher-order cases we resort to numerical integration using Runge-Kutta method with adaptive step-size algorithm. In order to analyze the model result, we perform numerical experiment for a vessel of 19190 tons under the beam wave of 1 m height and frequency 0.74 rad/s. Closer inspection in damping analysis reveals that viscous effect becomes significant for roll damping; whereas for yaw damping, contribution from added mass variation becomes significant.

scholarly journals Added Mass and Damping of a Vibrating Rod in Confined Viscous Fluids

1976 ◽  
Vol 43 (2) ◽  
pp. 325-329 ◽  
Author(s):  
S. S. Chen ◽  
M. W. Wambsganss ◽  
J. A. Jendrzejczyk
Keyword(s):  
Experimental Data ◽  
Experimental Study ◽  
Cylindrical Shell ◽  
Closed Form Solution ◽  
Added Mass ◽  
Form Solution ◽  
Viscous Fluids ◽  
Series Of Experiments ◽  
Theoretical Results ◽  
Good Agreement

This paper presents an analytical and experimental study of a cylindrical rod vibrating in a viscous fluid enclosed by a rigid, concentric cylindrical shell. A closed-form solution for the added mass and damping coefficient is obtained and a series of experiments with cantilevered rods vibrating in various viscous fluids is performed. Experimental data and theoretical results are in good agreement.

scholarly journals MHD Nanofluids in a Permeable Channel with Porosity

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 378 ◽  
Author(s):  
Ilyas Khan ◽  
Aisha Alqahtani
Keyword(s):  
Magnetic Parameter ◽  
Flow Direction ◽  
Perturbation Technique ◽  
Closed Form Solution ◽  
Form Solution ◽  
Convection Flow ◽  
Temperature Profiles ◽  
Uniform Temperature ◽  
One Dimensional ◽  
Physical Conditions

This paper introduces a mathematical model of a convection flow of magnetohydrodynamic (MHD) nanofluid in a channel embedded in a porous medium. The flow along the walls, characterized by a non-uniform temperature, is under the effect of the uniform magnetic field acting transversely to the flow direction. The walls of the channel are permeable. The flow is due to convection combined with uniform suction/injection at the boundary. The model is formulated in terms of unsteady, one-dimensional partial differential equations (PDEs) with imposed physical conditions. The cluster effect of nanoparticles is demonstrated in the C 2 H 6 O 2 , and H 2 O base fluids. The perturbation technique is used to obtain a closed-form solution for the velocity and temperature distributions. Based on numerical experiments, it is concluded that both the velocity and temperature profiles are significantly affected by ϕ . Moreover, the magnetic parameter retards the nanofluid motion whereas porosity accelerates it. Each H 2 O -based and C 2 H 6 O 2 -based nanofluid in the suction case have a higher magnitude of velocity as compared to the injections case.

Numerical Examination on Impact of Hall Current on Peristaltic Flow of Eyring-Powell Fluid under Ohmic-Thermal Effect with Slip conditions

2022 ◽  
Vol 18 ◽  
Author(s):  
Maria Yasin ◽  
Sadia Hina ◽  
Rahila Naz ◽  
Thabet Abdeljawad ◽  
Muhammad Sohail
Keyword(s):  
Thermal Effect ◽  
Hall Current ◽  
Perturbation Technique ◽  
Closed Form Solution ◽  
Form Solution ◽  
Regular Perturbation ◽  
Long Wavelength ◽  
Slip Conditions ◽  
Fluid Parameter ◽  
Opposite Behavior

Aims:: This article is intended to investigate and determine combined impact of Slip and Hall current on Peristaltic transmission of Magneto-hydrodynamic (MHD) Eyring-Powell fluid. Background: The hall term arises taking strong force-field under consideration. Velocity, thermal and concentration slip conditions are applied. Energy equation is modeled by considering Joule-thermal effect. To observe non-Newtonian behavior of fluid the constitutive equations of Eyring-Powell fluid is encountered. Objective: Flow is studied in a wave frame of reference travelling with velocity of wave. The mathematical modeling is done by utilizing adequate assumptions of long wavelength and low Reynolds number. Method: The closed form solution for momentum, temperature and concentration distribution is computed analytically by using regular perturbation technique for small fluid parameter(A). Results: Graphical results are presented and discussed in detail to analyze behavior of sundry parameters on flow quantities (i.e. velocity, temperature and concentration profile). It is noticed that Powell-Eyring fluid parameters (A,B) have a significant role on the outcomes. Conclusion: The fluid parameter A magnifies the velocity profile whereas, the other fluid parameter B shows the opposite behavior.

Squeeze Film Problems of Long Partial Journal Bearings for Non-Newtonian Couple Stress Fluids with Pressure-Dependent Viscosity

2011 ◽  
Vol 66 (8-9) ◽  
pp. 512-518 ◽  
Author(s):  
Jaw-Ren Lin ◽  
Li-Ming Chu ◽  
Chi-Ren Hung ◽  
Rong-Fang Lu
Keyword(s):  
Couple Stress ◽  
Load Capacity ◽  
Perturbation Technique ◽  
Closed Form Solution ◽  
Journal Bearings ◽  
Form Solution ◽  
Squeeze Film ◽  
Pressure Dependent Viscosity ◽  
Dependent Viscosity ◽  
Couple Stress Fluids

Abstract According to the experimental work of C. Barus in Am. J. Sci. 45, 87 (1893) [1], the dependency of liquid viscosity on pressure is exponential. Therefore, we extend the study of squeeze film problems of long partial journal bearings for Stokes non-Newtonian couple stress fluids by considering the pressure-dependent viscosity in the present paper. Through a small perturbation technique, we derive a first-order closed-form solution for the film pressure, the load capacity, and the response time of partial-bearing squeeze films. It is also found that the non-Newtonian couple-stress partial bearings with pressure-dependent viscosity provide better squeeze-film characteristics than those of the bearing with constant-viscosity situation.

Hydrodynamic coefficients of a vertical circular cylinder

1990 ◽  
Vol 17 (3) ◽  
pp. 302-310 ◽  
Author(s):  
Michael Isaacson ◽  
Thomas Mathai ◽  
Carol Mihelcic
Keyword(s):  
Circular Cylinder ◽  
High Frequency ◽  
Closed Form Solution ◽  
Added Mass ◽  
Offshore Structures ◽  
Form Solution ◽  
Ocean Engineering ◽  
Radiation Problem ◽  
The Vertical Distribution ◽  
Linear Radiation

The added mass and the damping coefficient of a large surface-piercing circular cylinder extending to the seabed and undergoing horizontal oscillations are described. A closed-form solution to the corresponding linear radiation problem is obtained by the use of eigenfunction expansions. Attention is given to the vertical distribution of these coefficients and to their high-frequency asymptotic behaviour. Comparisons are made with experimental measurements. The application to typical offshore structures is discussed. Key words: added mass, cylinders, damping, hydrodynamics, ocean engineering.

Nonlinear Vertical Vibration of Tension Leg Platforms with Homotopy Analysis Method

2015 ◽  
Vol 7 (3) ◽  
pp. 357-368 ◽  
Author(s):  
Arash Reza ◽  
Hamid M. Sedighi
Keyword(s):  
Differential Equation ◽  
Homotopy Analysis Method ◽  
Equations Of Motion ◽  
Closed Form Solution ◽  
Added Mass ◽  
Form Solution ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Mass Coefficient ◽  
Added Mass Coefficient

AbstractOne of the useful methods for offshore oil exploration in the deep regions is the use of tension leg platforms (TLP). The effective mass fluctuating of the structure which due to its vibration can be noted as one of the important issues about these platforms. With this description, dynamic analysis of these structures will play a significant role in their design. Differential equations of motion of such systems are nonlinear and providing a useful method for its analysis is very important. Also, the amount of added mass coefficient has a direct effect on the level of nonlinearity of partial differential equation of these systems. In this study, Homotopy analysis method has been used for closed form solution of the governing differential equation. Linear springs have been used for modeling the stiffness of this system and the effects of torsion, bending and damping of water have been ignored. In the study of obtained results, the effect of added mass coefficient has been investigated. The results show that increasing of this coefficient decreases the bottom amplitude of fluctuations and the system frequency. The obtained results from this method are in good agreement with the published results on the valid articles.

Interaction Between Two Bodies Translating in an Inviscid Fluid

1991 ◽  
Vol 35 (01) ◽  
pp. 1-8
Author(s):  
L. Landweber ◽  
A. T. Chwang ◽  
Z. Guo
Keyword(s):  
Translational Motion ◽  
Closed Form Solution ◽  
Added Mass ◽  
Form Solution ◽  
Circular Cylinders ◽  
Integral Approach ◽  
Inviscid Fluid ◽  
Added Masses ◽  
Two Bodies ◽  
Good Agreement

The equations of motion of two bodies in translational motion in an inviscid fluid at rest at infinity are expressed in Lagrangian form. For the case of one body stationary and the other approaching it in a uniform stream, an exact, closed-form solution in terms of added masses is obtained, yielding simple expressions for the velocity of the moving body as a function of its relative position and for the interaction forces. This solution is applied to the case of a rectangular cylinder approaching a cylindrical one, for which the added-mass coefficients had been previously obtained in a companion paper by an integral-equation procedure. In order to compare results with those in the literature, and to evaluate the accuracy of the present procedures, results were calculated for a pair of circular cylinders by these methods as well as by successive images. Very good agreement was found. Comparison with published results showed good agreement with the added mass but very poor agreement on the forces, including disagreement as to whether the forces were repulsive or attractive. The discrepancy is believed to be due to the omission of terms in the Bernoulli equation which was used to obtain the pressure distribution and then the force on a body. The Lagrangian formulation is believed to be preferable to the pressure-integral approach because it yields the hydrodynamic force directly in terms of the added masses and their derivatives, thus requiring the calculation of many fewer coefficients.

scholarly journals The Part-Through Surface Crack in an Elastic Plate

1972 ◽  
Vol 39 (1) ◽  
pp. 185-194 ◽  
Author(s):  
J. R. Rice ◽  
N. Levy
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Plane Strain ◽  
Surface Crack ◽  
Unit Length ◽  
Mathematical Formulation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Bending Loads

An elastic analysis is presented for the tensile stretching and bending of a plate containing a surface crack penetrating part-through the thickness, Fig. 1. The treatment is approximate, in that the two-dimensional generalized plane stress and Kirchhoff-Poisson plate bending theories are employed, with the part-through cracked section represented as a continuous line spring. The spring has both stretching and bending resistance, its compliance coefficients being chosen to match those of an edge cracked strip in plane strain. The mathematical formulation reduces finally to two-coupled integral equations for the thickness averaged force and moment per unit length along the cracked section. These are solved numerically for the case of a semi-elliptical part-through crack, with results compared to a simple but approximate closed-form solution. Extensive results are given for the stress intensity factor at the midpoint of the part-through crack for both remote tensile and bending loads on the plate. These results indicate that the stress-intensity factor is substantially lower, in general, than for a similarly loaded strip in plane strain with a crack of the same depth.

Dynamic Responses of Two Parallel Circular Cylinders in a Liquid

1975 ◽  
Vol 97 (2) ◽  
pp. 78-83 ◽  
Author(s):  
Shoei-Sheng Chen
Keyword(s):  
Approximate Solution ◽  
Equations Of Motion ◽  
Closed Form Solution ◽  
Added Mass ◽  
Form Solution ◽  
Dynamic Responses ◽  
Circular Cylinders ◽  
Steady State Responses ◽  
Fluid Coupling ◽  
State Responses

The problem of two parallel circular cylinders vibrating in a liquid is studied analytically. First, the equations of motion including fluid coupling are derived using the added mass concept. Then, a closed form solution and an approximate solution are obtained for free vibration. Finally, the steady-state responses of two cylinders subjected to harmonic excitations are presented. The results of this study illustrate the significance of the interaction of two structures in a liquid.

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