Nonlinear Wave Loads Affected by the Low-Frequency Oscillations in the Horizontal Plane

2003 ◽  
Author(s):  
Takeshi Kinoshita ◽  
Weiguang Bao
Keyword(s):  
Nonlinear Wave ◽  
Perturbation Expansion ◽  
Low Frequency ◽  
Hydrodynamic Pressure ◽  
Wave Loads ◽  
Slow Oscillations ◽  
Low Frequency Oscillations ◽  
Wave Drift ◽  
Small Parameters ◽  
Wave Drift Damping

To investigate the effects of the low-frequency oscillations on the nonlinear wave loads, the interaction of the low-frequency oscillations with the ambient wave fields is considered. The frequency of the slow oscillations is assumed to be much smaller than the wave frequency. Perturbation expansion based on two small parameters, i.e. the incident wave amplitude and the low frequency, is performed to simplify the problem. Nonlinear wave loads including the wave drift damping and wave drift added mass are evaluated by the integration of the hydrodynamic pressure over the instantaneous wetted body surface. The problem is solved for a uniform circular cylinder by means of the Green’s theorem and semi-analytical solutions are presented. The far field conditions for each order of potentials are proposed to ensure the existence of a unique solution. The restriction on the validation of the solutions is discussed.

Nonlinear Wave Loads Acting on Cylinder Array Slowly Oscillating in Diffraction and Radiation Wave Fields

2005 ◽  
Author(s):  
Weiguang Bao ◽  
Takeshi Kinoshita ◽  
Motoki Yoshida
Keyword(s):  
Nonlinear Wave ◽  
Perturbation Expansion ◽  
Low Frequency ◽  
Added Mass ◽  
Wave Loads ◽  
Wave Fields ◽  
Wave Drift ◽  
Cylinder Array ◽  
Radiation Wave ◽  
Low Frequency Motion

The problem of a circular cylinder array slowly oscillating in both diffraction and radiation wave fields is considered in the present work. As a result of the interaction between the wave fields and the low-frequency motion, nonlinear wave loads may be separated into the so-called wave-drift added mass and damping. They are force components proportional to the square of the wave amplitude but in phase of the acceleration and velocity of the low-frequency motion respectively. The frequency of the slow oscillation is assumed to be much smaller than the wave frequency. Perturbation expansion based on two time scales and two small parameters is performed to the order to include the effects of the acceleration of the low-frequency motion. Solutions to these higher order potentials are suggested in the present work. Wave loads including the wave drift added mass and damping are evaluated by the integration of the hydrodynamic pressure over the instantaneous wetted body surface.

Wave-Drift Added Mass of a Cylinder Array Free to Respond to the Incident Waves

2002 ◽  
Author(s):  
Takeshi Kinoshita ◽  
Weiguang Bao ◽  
Motoki Yoshida ◽  
Kazuko Ishibashi
Keyword(s):  
Perturbation Expansion ◽  
Low Frequency ◽  
Hydrodynamic Pressure ◽  
Added Mass ◽  
Floating Body ◽  
Wave Loads ◽  
Alternative Source ◽  
Wave Drift ◽  
Cylinder Array ◽  
Incident Waves

Conventional linear added mass and damping can be obtained when a floating body is forced to oscillate in the calm water. However, with the presence of the incident waves, there exists an alternative source of added mass and damping caused by the nonlinear interactions between waves and low-frequency oscillations. Proportional to the square of the wave amplitude, they are called the wave drift added mass and the wave drift damping. The problem of a circular cylinder array slowly oscillating in both diffraction and radiation wave fields is considered in the present work. The frequency of the low-frequency oscillation is assumed to be much smaller than the wave frequency. Perturbation expansion based on two time scales is performed to simplify the problem. Wave loads including the wave drift added mass are formulated by integration of the hydrodynamic pressure over the instantaneous wetted body surface.

New Methods to Solve High Order Potential Used in Calculating Non-Linear Wave Loads

2006 ◽  
Author(s):  
Yasunori Nihei ◽  
Weiguang Bao ◽  
Takeshi Kinoshita
Keyword(s):  
Perturbation Expansion ◽  
Low Frequency ◽  
The Body ◽  
Body Motion ◽  
Moving Frame ◽  
Linear Wave ◽  
Wave Loads ◽  
Wave Drift ◽  
Non Linear ◽  
Low Frequency Motion

In the present study, non-linear wave loads such as the wave-drift force, wave-drift damping and wave-drift added mass, acting on the body is considered based on the potential theory. To investigate non-linear wave loads, consistent perturbation expansion by means of two small parameters, i.e. the incident wave slope and the low frequency body motion, is performed on a moving frame (body-fixed) coordinate system. To avoid complicated free surface integrals as much as possible, new approach for the higher order potential in the interaction problem of low frequency motion and waves is suggested in the present work. Instead of integrals, derivative operators are defined to obtain special solutions efficiently.

Nonlinear Hydrodynamic Forces on an Accelerated Body in Waves

2005 ◽  
Vol 127 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Motoki Yoshida ◽  
Takeshi Kinoshita ◽  
Weiguang Bao
Keyword(s):  
Perturbation Analysis ◽  
Low Frequency ◽  
Multiple Scale ◽  
Added Mass ◽  
Floating Body ◽  
Floating Bodies ◽  
Low Frequency Oscillations ◽  
Wave Drift ◽  
Decay Test ◽  
Field Radiation

Wave-drift added mass results from nonlinear interactions between waves and low-frequency oscillatory motions of a floating body, in the presence of incident waves. In previous works, wave-drift damping which is the component of wave-drift force in phase with the velocity of low-frequency oscillations was investigated mainly based on a quasi-steady analysis. However, investigations related to wave-drift added mass, the component in phase with acceleration, were very few. In this paper, wave-drift added mass is derived directly from a perturbation analysis with two small parameters and two time scales, using a Cartesian coordinate system that follows the low-frequency oscillations, dynamic oscillation model has been used. Especially, the method to solve higher-order potentials, which are necessary for evaluation of wave-drift added mass, is presented. Analytical solutions and calculated results of wave-drift added mass, and far field radiation conditions for each order of potentials are obtained. Also, wave-drift added mass of floating bodies has been systematically measured from a slowly forced oscillation test or a free decay test in waves. Experimental results are compared with calculated results. Then, for a supplement, the secular behavior that some velocity potentials show is discussed. Applying a multiple scale perturbation analysis to one of these problems, a nonsecular solution is obtained.

On the Increased Damping of a Moored Body During Low-Frequency Motions in Waves

1988 ◽  
Vol 110 (4) ◽  
pp. 348-354 ◽  
Author(s):  
S. Nakamura ◽  
K. Saito ◽  
M. Takagi
Keyword(s):  
Free Oscillation ◽  
Estimation Method ◽  
Low Frequency ◽  
Equation Of Motion ◽  
Two Dimensional ◽  
Wave Groups ◽  
Wave Drift ◽  
Analytical Estimation ◽  
Wave Drift Damping ◽  
Low Frequency Motion

An estimation method for the increased damping on a moored body in waves which allow simulation of the decay increase of low-frequency motion in waves is described. Emphasis is put on the analytical estimation method for the increased damping due to waves (wave drift damping) on a moored body during low-frequency motion. The estimated increased damping is compared with that of free oscillation tests in waves, and it is shown that the estimation method presented herein is acceptable qualitatively. The low-frequency resonant sway motions of a two-dimensional moored body in regular wave groups are also compared, and the numerical results show a tendency similar to the experiments when the wave drift damping is included in the equation of motion.

Non-Linear Wave Forces Acting on a Body of Arbitrary Shape Slowly Oscillating in Waves

2005 ◽  
Author(s):  
Yasunori Nihei ◽  
Takeshi Kinoshita ◽  
Weiguang Bao
Keyword(s):  
Low Frequency ◽  
The Body ◽  
Coordinate Frame ◽  
Wave Forces ◽  
Linear Wave ◽  
Wave Loads ◽  
Low Frequency Oscillation ◽  
Wave Drift ◽  
Non Linear ◽  
Low Frequency Motion

In the present study, non-linear wave loads such as the wave drift force, wave drift damping and wave drift added mass, acting on a moored body is evaluated based on the potential theory. The body is oscillating at a low frequency under the non-linear excitation of waves. The problem of interaction between the low-frequency oscillation of the body and ambient wave fields is considered. A moving coordinate frame following the low frequency motion is adopted. Two small parameters, which measure the wave slope and the frequency of slow oscillations (compared with the wave frequency) respectively, are used in the perturbation analysis. So obtained boundary value problems for each order of potentials are solved by means of the hybrid method. The fluid domain is divided into two regions by an virtual circular cylinder surrounding the body. Different approaches, i.e. boundary element method and eigen-function expansion, are applied to these two regions. Calculated nonlinear wave loads are compared to the semi-analytical results to validate the present method.

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