• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.173-187
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• 2013

This paper studies the properties of solutions of the Riccati equation arising from the quadratic optimal control problem of the general damped second order system. Using the semigroup theory, we establish the weak differential characterization of the Riccati equation for a general class of the second order distributed systems with arbitrary damping terms.

• Journal of Ocean Engineering and Technology
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• v.19 no.3
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• pp.25-30
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• 2005

To predict rolling performance for a barge-type FPSO, the evaluation of correct nonlinear roll damping is critical. The square section of FPSO causes a considerable viscous damping effect. Free roll decay tests were carried out to estimate nonlinear roll damping for a barge-type FPSO, under three different conditions. The roll motion RAO was deduced from model tests in the wave condition of the wideband spectrum. In numerical calculation, the quadratic damping was considered as equivalent linear damping, using the results of free roll decay test. Tested roll performance in the JONSWAP wave spectrum was compared with numerical results. These two results shaw good agreement, in spite of the proximity of peak wave period and roll natural period.

• Journal of Mechanical Science and Technology
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• v.17 no.3
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• pp.457-466
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• 2003

In this paper, the numerical finite element formulations were derived for the linearized Navier-Stokes' equations with assumptions of two-dimensional incompressible, homogeneous viscous fluid field, and small oscillation and the FAMD (Fluid Added Mass and Damping) code was developed for practical applications calculating the fluid added mass and damping. In formulations, a fluid domain is discretized with C$\^$0/-type quadratic quadrilateral elements containing eight nodes using a mixed interpolation method, i.e., the interpolation function for the velocity variable is approximated by a quadratic function based on all eight nodal points and the interpolation function for the pressure variable is approximated by a linear function based on the four nodal points at vertices. Using the developed code, the various characteristics of the fluid added mass and damping are investigated for the concentric cylindrical shell and the actual hexagon arrays of the liquid metal reactor cores.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2004.11a
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• pp.183-187
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• 2004

To predict rolling performance for a barge-type FPSO, the evaluation of correct nonlinear roll damping is critical. The squall section of FPSO causes a fair amount of viscous damping effect. Free roll decoy tests were conducted to estimate nonlinear roll damping for a barge-typ FPSO of three different loading conditions. The roll motion RAO was deduced by model tests in the wave condition of wideband spectrum. In numerical calculation, the quadratic damping was considered as equivalent linear damping using the results of free roll decay test. Tested roll performance in JONSWAP wave spectrum was compared with numerical results. These two results show good agreement, in spite of proximity in peak wave period and roll natural period.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2006.10a
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• pp.134-143
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• 2006

Out of all types of motions the critical motions leading to capsize is roll. The dynamic amplification in case of roll motion may be large for ships as roll natural frequency generally falls within the frequency range of wave energy spectrum typical used for estimation of motion spectrum. Roll motion is highly non-linear in nature. Den are various representations of non-linear damping and restoring available in literature. In this paper an uncoupled non-linear roll equations with three representation of damping and cubic restoring term is solved using a perturbation technique. Damping moment representations are linear plus quadratic velocity damping, angle dependant damping and linear plus cubic velocity dependant damping. Numerical value of linear damping coefficient is almost same for all types but non-linear damping is different. Linear and non-linear damping coefficients are obtained form free roll decay tests. External rolling moment is assumed as deterministic with sinusoidal form. Maximum roll amplitude of non-linear roll equation with various representations of damping is calculated using analytical procedure and compared with experimental results, which are obtained form forced tests in regular waves by varying frequency with three wave heights. Experiments indicate influence of non-linearity at resonance frequency. Both experiment and analytical results indicates increase in maximum roll amplitude with wave slope at resonance. Analytical results are compared with experiment results which indicate maximum roll amplitude analytically obtained with angle dependent and cubic velocity damping are equal and difference from experiments with these damping are less compared to non-linear equation with quadratic velocity damping.

• Journal of the Society of Naval Architects of Korea
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• v.52 no.6
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• pp.460-470
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• 2015

In general ships and FPSOs, roll damping is very small and consequently roll motion is very large at the roll resonance frequency. Proper evaluation of the roll damping coefficient at the resonance frequency is an important task in the study of roll motion and usually it is done by the analysis of free roll decay tests. The relative decrement method based on energy relation has been used mainly for the evaluation of roll damping coefficient from the roll decay test so far. As another method, the logarithmic decrement method based on equivalent linear decay assumption can be used for the same purpose and it is relatively simple. In this paper, both of the relative decrement method and the logarithmic decrement method are used for the evaluation of roll damping coefficient including quadratic damping from the free roll decay tests, and their results are cross-checked for verifying the obtained damping coefficients. Through applications to a box-type floating body equiped with bilge keels, it is shown that the two methods give almost the same damping coefficients in a practical view point and the cross-check of their results is to be a good tool to prevent a possible error. And also the quantitative effects of the bilge keels on the roll damping of box-type floating body are shown and discussed.

• Journal of Ocean Engineering and Technology
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• v.32 no.1
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• pp.1-8
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• 2018

In order to analyze the response of the offshore structure numerically, the linear potential theory is generally applied for simplicity, and only the radiation damping is considered among various damping forces. Therefore, the results of a numerical simulation can be different from the motion of the structure in a real environment. To reduce the differences between the simulation results and experimental results, the viscous damping, which affects the motion of the structure, is also taken into account. The appropriate damping model is essential for the numerical simulation in order to obtain precise responses of the offshore structure. In this study, various damping models such as linear or quadratic damping and the nonlinear drag force from numerous slender bodies were used to simulate the free decay motion of the platform, and its characteristics were confirmed. The optimized damping model was found by comparing the simulation results to the experimental results. The hydrodynamic forces and wave exciting forces of the structure were obtained using WAMIT, and the free decay test was simulated using OrcaFlex. A free decay test of the scale model was performed by KRISO.

• Ocean Systems Engineering
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• v.5 no.2
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• pp.55-76
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• 2015

Of all the six degrees of freedom, the roll motion of a ship is the most poorly understood and displays complicated phenomena. Due to the low potential wave damping at the natural frequency, the effective analysis of ship roll dynamics comes down to the accurate estimation of the viscous roll damping. This paper provides overview of the importance of roll damping and an extensive literature review of the various viscous roll damping prediction methods applied by researchers over the years. The paper also discusses in detail the current state of the art estimation of viscous roll damping for ship shaped structures. A computer code is developed based on this method and its results are compared with experimental data to demonstrate the accuracy of the method. While some of the key references describing this method are not available in English, some others have been found to contain typographic errors. The objective of this paper is to provide a comprehensive summary of the state of the art method in one place for future reference.

• Structural Engineering and Mechanics
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• v.87 no.1
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• pp.57-68
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• 2023

Response spectrum method is still an effective approach for the design of buildings with supplemental dampers. In practice, complex complete quadratic combination (CCQC) rule is always used in the response spectrum method to consider the effect of non-classical damping. The conventional CCQC rule is based on exact complex mode vectors. Sometimes the calculated complex mode vectors may be not excited by the external loading and errors in the structural responses always arise due to the mode truncation. Load-dependent Ritz (LDR) vectors are associated with the external loading and LDR vectors not excited can be automatically excluded. Also, contributions of higher modes are implicitly contained in the LDR vectors in terms of static responses. To improve the calculation efficiency and accuracy, LDR vectors are introduced in the CCQC rule in the present study. Firstly, the generation procedure of LDR vectors suitable for non-classical damping system is presented. Compared to the conventional LDR vectors, the LDR vectors herein are complex-valued and named as complex LDR (CLDR) vectors. Based on the CLDR vectors, the CCQC rule is then rederived and an improved response spectrum method is developed. Finally, the effectiveness of the proposed method in this paper is verified through three typical non-classical damping buildings. Numerical results show that the CLDR vector is superior to the complex mode with the same number in the calculation. Since the generation of CLDR vectors requires less computational cost and storage space, the method proposed in this paper offers an attractive alternative, especially for structures with a large number of degrees of freedom.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.4
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• pp.351-363
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• 2004

Equation of motion of non conservative system considering mass matrix, elastic stiffness matrix, load correction stiffness matrix by circulatory force's direction change and Winkler and Pasternak foundation stiffness matrix is derived. Also stability analysis due to the divergence and flutter loads is performed. And the influence of internal and external damping coefficient on flutter load is investigated applying the quadratic eigen problem solution. Additionally the influence of non-conservative force's direction parameter, internal and external damping and Winkler and Pasternak foundation on the critical load of Beck's and Leipholz's and Hauger's columns are investigated.