Comparisons of Simulation Methods for Motions of a Moored Body in Waves

1985 ◽  
Vol 107 (1) ◽  
pp. 34-41
Author(s):  
M. Takagi ◽  
K. Saito ◽  
S. Nakamura
Keyword(s):  
Wave Theory ◽  
Simulation Methods ◽  
Convolution Integral ◽  
Linear Water Wave Theory ◽  
Initial Stage ◽  
Constant Coefficients ◽  
Exciting Forces ◽  
Linear Differential ◽  
Experimental Values ◽  
The Time Domain

Based on the linear water wave theory, numerical simulations are carried out for motions in waves of a body moored by a nonlinear-type mooring system. Numerical results obtained by using the equation of motion described in the time domain with a convolution integral (C.I. method) are compared with those of the second-order linear differential equation with constant coefficients (C. C. method). These results are also compared with experimental values measured from the initial stage when the action of exciting forces starts and the validity of C.I. method is discussed.

A Research on Characteristics of Responses of a Floating Structure in Tsunami

2004 ◽  
Author(s):  
Koichi Masuda ◽  
Tomoki Ikoma ◽  
Maki Uchida ◽  
Akira Takeda
Keyword(s):  
Wave Theory ◽  
Floating Body ◽  
Present System ◽  
Convolution Integral ◽  
Floating Bodies ◽  
Floating Structure ◽  
Exciting Forces ◽  
Mooring Forces ◽  
Analysis System ◽  
Present Simulation

The objective of present paper are to establish the practical numerical analysis system for responses of motions and mooring forces on a floating structure induced by Tsunami and to clarify the characteristics of responses on floating bodies in tsunami. In the present analysis system, the initial tsunami profile is evaluated by Mansinha-Smylie’s Method and propagating tsunami profiles are calculated by linear long wave theory and also the tsunami exciting forces on floating body are computed by the numerical wave tank based on VOF method [5] and then the motions and mooring tether forces due to Tsunami on floating body are predicted by the convolution integral method. The usefulness of present system is confirmed by comparing with the experimental results on Tsunami exciting forces on floating bodies. The responses of floating body due to tsunami using fault models of Tokai and Tonankai earthquakes are computed by using the present simulation system so that the characteristics of responses on floating bodies are examined and are clarified.

scholarly journals A graphical solution of a differential equation with application to hill’s treatment of nerve excitation

1937 ◽  
Vol 123 (832) ◽  
pp. 382-395 ◽  
Keyword(s):  
Viscous Medium ◽  
Graphical Solution ◽  
Initial Value ◽  
First Order ◽  
Rate Dependent ◽  
Monomolecular Reaction ◽  
Constant Coefficients ◽  
Linear Differential ◽  
Physical And Chemical ◽  
Nerve Excitation

Linear differential equations with constant coefficients are very common in physical and chemical science, and of these, the simplest and most frequently met is the first-order equation a dy / dt + y = f(t) , (1) where a is a constant, and f(t) a single-valued function of t . The equation signifies that the quantity y is removed at a rate proportional to the amount present at each instant, and is simultaneously restored at a rate dependent only upon the instant in question. Familiar examples of this equation are the charging of a condenser, the course of a monomolecular reaction, the movement of a light body in a viscous medium, etc. The solution of this equation is easily shown to be y = e - t / a { y 0 = 1 / a ∫ t 0 e t /a f(t) dt , (2) where y 0 is the initial value of y . In the case where f(t) = 0, this reduces to the well-known exponential decay of y .

The Wave Theory of the Electron

1928 ◽  
Vol 24 (4) ◽  
pp. 501-505 ◽  
Author(s):  
J. M. Whittaker
Keyword(s):  
Wave Function ◽  
Differential Equations ◽  
Fourth Order ◽  
Commutative Algebra ◽  
Wave Theory ◽  
Wave Functions ◽  
Linear Differential Equations ◽  
Wave Mechanics ◽  
First Order ◽  
Linear Differential

In two recent papers Dirac has shown how the “duplexity” phenomena of the atom can be accounted for without recourse to the hypothesis of the spinning electron. The investigation is carried out by the methods of non-commutative algebra, the wave function ψ being a matrix of the fourth order. An alternative presentation of the theory, using the methods of wave mechanics, has been given by Darwin. The four-rowed matrix ψ is replaced by four wave functions ψ1, ψ2, ψ3, ψ4 satisfying four linear differential equations of the first order. These functions are related to one particular direction, and the work can only be given invariance of form at the expense of much additional complication, the four wave functions being replaced by sixteen.

Numerical Simulation on Mooring Performance of LNG-FPSO System in Realistic Seas

2005 ◽  
Author(s):  
Yoshiyuki Inoue ◽  
Md. Kamruzzaman
Keyword(s):  
Time Domain ◽  
Oil And Gas ◽  
Three Dimensional ◽  
Time Domain Analysis ◽  
Analysis Tool ◽  
Motion Response ◽  
Non Linear ◽  
Floating System ◽  
Exciting Forces ◽  
The Time Domain

The LNG-FPSO concept is receiving much attention in recent years, due to its active usage to exploit oil and gas resources. The FPSO offloads LNG to an LNG carrier that is located close to the FPSO, and during this transfer process two large vessels are in close proximity to each other for daylong periods of time. Due to the presence of neighboring vessel, the motion response of both the vessels will be affected significantly. Hydrodynamic interactions related to wave effects may result in unfavorable responses or the risk of collisions in a multi-body floating system. Not only the motion behavior but also the second order drift forces are influenced by the neighboring structures due to interactions of the waves among the structures. A study is made on the time domain analysis to assess the behavior and the operational capability of the FPSO system moored in the sea having an LNG carrier alongside under environmental conditions such as waves, wind and currents. This paper presents an analysis tool to predict the dynamic motion response and non-linear connecting and mooring forces on a parallel-connected LNG-FPSO system due to non-linear exciting forces of wave, wind and current. Simulation for the mooring performance is also investigated. The three-dimensional source-sink technique has been applied to obtain the radiation forces and the transfer function of wave exciting forces on floating multi-bodies. The hydrodynamic interaction effect between the FPSO and the LNG carrier is included to calculate the hydrodynamic forces. For the simulation of a random sea and also for the generation of time depended wind velocity, a fully probabilistic simulation technique has been applied. Wind and current loads are estimated according to OCIMF. The effects of variations in wave, wind and current loads and direction on the slowly varying oscillations of the LNG and FPSO are also investigated in this paper. Finally, some conclusions are drawn based on the numerical results obtained from the present time domain simulations.

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