Fast Frequency-Domain Algorithm for Estimating the Dynamic Wind-Induced Response of Large-Span Roofs Based on Cauchy’s Residue Theorem

2018 ◽  
Vol 18 (03) ◽  
pp. 1850037 ◽  
Author(s):  
Ning Su ◽  
Zhenggang Cao ◽  
Yue Wu
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Rational Functions ◽  
Induced Response ◽  
Response Analysis ◽  
Residue Theorem ◽  
Coupling Effects ◽  
Large Span ◽  
Modal Coupling ◽  
Cauchy’S Residue Theorem

Wind-induced response analysis is an important process in the design of large-span roofs. Conventional time-domain methods are computationally more expensive than frequency-domain algorithms; however, the latter are not as accurate because of the ill-treatment of the modal coupling effects. This paper revisited the derivations of the frequency-domain algorithm and proposed a fast algorithm for estimating the dynamic wind-induced response considering duly the modal coupling effects. With the wind load cross-spectra modeled by rational functions, closed-form solutions to the frequency-domain integrals can be calculated by Cauchy’s residue theorem, rather than by numerical integration, thereby reducing the truncation errors and enhancing the efficiency of computation. The algorithm is applied to the analysis of a grandstand roof and a spherical dome. Through comparison with time domain analyses results, the algorithm is proved to be reliable. A criterion of the coupling modal combination was suggested based on the cumulative modal contribution rate of over 70%.

The Effects of Inner-Liquid Motion on LNG Vessel Responses

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
S. J. Lee ◽  
M. H. Kim
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Surface Profile ◽  
Ship Motion ◽  
Liquid Sloshing ◽  
Diffraction Radiation ◽  
Time Domain Simulation ◽  
Coupling Effects ◽  
The Time Domain ◽  
Vessel Motion

The coupling and interactions between ship motion and inner-tank sloshing are investigated by a potential-viscous hybrid method in the time domain. For the time-domain simulation of vessel motion, the hydrodynamic coefficients and wave forces are obtained by a potential-theory-based 3D diffraction/radiation panel program in the frequency domain. Then, the corresponding simulations of motions in the time domain are carried out using the convolution-integral method. The liquid sloshing in a tank is simulated in the time domain by a Navier–Stokes solver. A finite difference method with SURF scheme assuming the single-valued free-surface profile is applied for the direct simulation of liquid sloshing. The computed sloshing forces and moments are then applied as external excitations to the ship motion. The calculated ship motion is in turn inputted as the excitation for liquid sloshing, which is repeated for the ensuing time steps. For comparison, we independently developed a 3D panel program for linear inner-fluid motions, and it is coupled with the vessel-motion program in the frequency domain. The developed computer programs are applied to a barge-type floating production storage and offloading (FPSO) hull equipped with two partially filled tanks. The time-domain simulation results show reasonably good agreement when compared with Maritime Research Institute Netherlands (MARIN’s) experimental results. The frequency-domain results qualitatively reproduce the trend of coupling effects, but the peaks are in general overpredicted. It is seen that the coupling effects on roll motions appreciably change with filling level. The most pronounced coupling effects on roll motions are the shift or split of peak frequencies. The pitch motions are much less influenced by the inner-fluid motion compared with roll motions.

Understanding the Dynamic Coupling Effects in Deep Water Floating Structures Using a Simplified Model

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Ying Min Low ◽  
Robin S. Langley
Keyword(s):  
Frequency Domain ◽  
Deep Water ◽  
Time Domain ◽  
Low Frequency ◽  
Wave Frequency ◽  
Computational Time ◽  
Coupled Analysis ◽  
Floating Platform ◽  
Coupling Effects ◽  
Mooring Lines

The global dynamic response of a deep water floating production system needs to be predicted with coupled analysis methods to ensure accuracy and reliability. Two types of coupling can be identified: one is between the floating platform and the mooring lines/risers, while the other is between the mean offset, the wave frequency, and the low frequency motions of the system. At present, it is unfeasible to employ fully coupled time domain analysis on a routine basis due to the prohibitive computational time. This has spurred the development of more efficient methods, including frequency domain approaches. A good understanding of the intricate coupling mechanisms is paramount for making appropriate approximations in an efficient method. To this end, a simplified two degree-of-freedom system representing the surge motion of a vessel and the fundamental vibration mode of the lines is studied for physical insight. Within this framework, the frequency domain equations are rigorously formulated, and the nonlinearities in the restoring forces and drag are statistically linearized. The model allows key coupling effects to be understood; among other things, the equations demonstrate how the wave frequency dynamics of the mooring lines are coupled to the low frequency motions of the vessel. Subsequently, the effects of making certain simplifications are investigated through a series of frequency domain analyses, and comparisons are made to simulations in the time domain. The work highlights the effect of some common approximations, and recommendations are made regarding the development of efficient modeling techniques.

A Preliminary Study of a Rigid Semi-Submersible Fish Farm for Open Seas

2017 ◽  
Author(s):  
Lin Li ◽  
Muk Chen Ong
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Time Domain Analysis ◽  
Fish Farm ◽  
Response Analysis ◽  
Frequency Domain Method ◽  
Mooring System ◽  
Viscous Effects ◽  
Support Structure ◽  
Mooring Lines

The development of reliable fish farm structures for open seas becomes more and more important. One of the challenges is to design a robust structure to withstand the harsh offshore environmental loads. This paper investigates a semi-submersible type offshore fish farm system for open seas. This system consists of a semi-submersible support structure with pontoons and braces, a catenary mooring system and net cages. The support structure is designed to be rigid to resist severe offshore conditions. A preliminary hydrodynamic and response analysis is carried out for this concept. The linear hydrodynamic properties using different composite models with panel and Morison elements are computed. Based on the hydrodynamic analysis, linearised frequency-domain and coupled time-domain analysis are performed to predict the extreme motions of the support structure and the extreme tensions in the mooring lines. The results indicate that the frequency-domain method underestimates the extreme responses, and the couplings between the structure and the mooring system need to be considered in the time-domain. Responses using various hydrodynamic models are also compared to evaluate the influences of the viscous effects from the pontoons and the nets of this fish farm concept.

The Effects of Tank Sloshing on LNG Vessel Responses

2007 ◽  
Author(s):  
S. J. Lee ◽  
M. H. Kim ◽  
D. H. Lee ◽  
Y. S. Shin
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Ship Motion ◽  
Liquid Sloshing ◽  
Diffraction Radiation ◽  
Time Domain Simulation ◽  
Coupling Effects ◽  
The Time Domain ◽  
Vessel Motion ◽  
Tank Sloshing

The coupling and interactions between ship motion and inner-tank sloshing are investigated by a potential-viscous hybrid method in time domain. For the time domain simulation of vessel motion, the hydrodynamic coefficients and wave forces are obtained by a potential-theory-based 3D diffraction/radiation panel program in frequency domain. Then, the corresponding simulations of motions in time domain are carried out using the convolution-integral method. The liquid sloshing in a tank is simulated in time domain by a Navier-Stokes solver. A finite difference method with SURF scheme assuming the single-valued free surface profile is applied for the direct simulation of liquid sloshing. The computed sloshing forces and moments are then applied as external excitations to the ship motion. The calculated ship motion is in turn inputted as the excitation for liquid sloshing, which is repeated for the ensuing time steps. For comparison, we independently developed a 3D panel program for linear inner-fluid motions and it is coupled with the vessel motion program in the frequency domain. The developed computer programs are applied to a barge-type FPSO hull equipped with two partially filled tanks. The time-domain simulation results show reasonably good agreement when compared with MARIN’s experimental results. The frequency-domain results qualitatively reproduce the trend of coupling effects but the peaks are in general over-predicted. It is seen that the coupling effects on roll motions appreciably change with filling level. The most pronounced coupling effects on roll motions are the shift or split of peak frequencies. The pitch motions are much less influenced by the inner-fluid motion compared to roll motions.

Dominant Modals of Wind-Induced Vibration Response for Spherical Kiewitt Cable Dome

2014 ◽  
Vol 1065-1069 ◽  
pp. 1156-1159 ◽  
Author(s):  
De Min Wei ◽  
Di Li ◽  
Ya Qing Liu
Keyword(s):  
Frequency Domain ◽  
Correlation Coefficients ◽  
Frequency Domain Analysis ◽  
Vibration Response ◽  
Induced Response ◽  
Response Analysis ◽  
Computational Results ◽  
Cable Dome ◽  
Wind Induced Vibration ◽  
Wind Induced Vibration Response

Correlation coefficients of mode shape between higher frequency modes and lower frequency modes are given. Then 17 high modes were initially selected as the dominant high modes in the analysis of wind-induced response, and cumulative mode correlation was used to judge the rationality of the method of selecting dominant high modals, so dominant modals of wind-induced response analysis are constructed. Based on these, the wind-induced vibration response of spherical Kiewitt cable dome was analyzed in frequency domain using CQC method. Through analyses of computational results, it is found that the selecting method of dominant modals by using the mode correlation coefficient can be applied in frequency domain analysis for wind-induced vibration response of cable dome structures. If the first 100 modals are considered into the analysis, the computational results obtained will be high precision.

Hydrodynamic Response Analysis of Combined Spar Wind Turbine and Fish Cage for Offshore Fish Farms

2020 ◽  
Vol 20 (09) ◽  
pp. 2050104
Author(s):  
Y. I. Chu ◽  
C. M. Wang
Keyword(s):  
Wind Turbine ◽  
Frequency Domain ◽  
Time Domain ◽  
Fish Farming ◽  
Fish Farm ◽  
Constant Current ◽  
Response Analysis ◽  
Comparison Study ◽  
Mooring Lines ◽  
Hydrodynamic Response

This paper is concerned with the hydrodynamic response of a novel offshore fish farm that combines a floating spar wind turbine and a fish cage (named as COSPAR for brevity). The open net steel cage is octagonal in shape with a partially porous wave fence at its top end to attenuate wave energy for a calm fish farming environment as well as to keep predators out. The deep draught spar is made from concrete for its bottom half and from steel for its top half. The spar carries a control unit and a 1[Formula: see text]MW wind turbine that provides the required power to operate the offshore salmon fish farm. The COSPAR fish cage has four catenary chains as mooring lines attached to mid length of the spar (outside the fish cage) so as to mitigate tension force in the mooring lines and to reduce the benthic footprint. ANSYS Design Modeler and Aqwa are used to perform the hydrodynamic response analysis of free-floating condition of COSPAR in the frequency domain and coupled analysis involving COSPAR and the mooring lines in the frequency domain and time domain. Environmental conditions, representing 5-year, 20-year and 50-year wave return periods with a constant current flow at an exposed fish farming site in Storm Bay of Tasmania, Australia, are adopted for the analyses. A comparison study is made against having a floating fish cage only (i.e. without the bottom half concrete of the spar) with four catenary chains attached to side vertical columns of the cage so that the fish cage behaves like a semi-submersible cage. Based on the comparison study, the COSPAR fish cage shows enhanced hydrodynamic responses in the following respects: (1) more stable motion responses in heave and pitch against wave and current forces, (2) less susceptible to the viscous damping when it is assumed by a linearized drag force of Morison elements in the frequency domain and (3) reduction of tension forces in the mooring lines. Interestingly, the pitch motion response of COSPAR fish cage in the frequency domain is in close agreement with the time domain result due to its greater pitching stiffness that reduces nonlinear effects from viscous drag and mooring interaction.

A Simplified Model for the Study of Dynamic Coupling Effects in Deepwater Floating Structures

2005 ◽  
Author(s):  
Ying Min Low ◽  
Robin S. Langley
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Low Frequency ◽  
Wave Frequency ◽  
Computational Time ◽  
Coupled Analysis ◽  
Floating Platform ◽  
Coupling Effects ◽  
Fundamental Vibration ◽  
Mooring Lines

As the exploitation of hydrocarbon moves towards deeper waters, the global dynamic response of a floating production system needs to be predicted with coupled analysis methods to ensure accuracy and reliability. Two types of coupling can be identified: one is between the floating platform and the mooring lines/risers, while the other is between the mean offset, the wave frequency and the low frequency motions of the system. At present, it is unfeasible to employ fully coupled time domain analysis on a routine basis due to prohibitive computational time. This has spurred the development of more efficient methods that account for the various couplings, including frequency domain approaches. It is paramount for the complex coupling mechanisms to be well understood before appropriate simplifications and assumptions can be made. In this paper, a simplified two degree-of-freedom system representing the surge motion of a vessel and the fundamental vibration mode of the lines is examined which captures the important underlying physics. Within this framework, the frequency domain equations are rigorously formulated, and the nonlinearities in the restoring forces and drag are stochastically linearized. The model allows key coupling effects to be identified: among other things, the equations demonstrate how the wave frequency dynamics of the mooring lines are coupled to the low frequency motions of the vessel. Subsequently, the effects of making certain simplifications are investigated through a series of frequency domain spectral analyses, and comparisons are made to simulations in the time domain. The work highlights the effect of certain common approximations, and recommendations are made regarding the development of efficient modeling techniques.

Dominant mode selection and modal coupling analysis for wind-induced response of long-span roofs

2016 ◽  
Vol 20 (4) ◽  
pp. 616-628
Author(s):  
Yuxue Li ◽  
Kai Shi ◽  
Qingshan Yang ◽  
Yuji Tian
Keyword(s):  
Mode Selection ◽  
Structural Response ◽  
Combination Method ◽  
Induced Response ◽  
Response Analysis ◽  
Square Root ◽  
Coupling Analysis ◽  
Modal Strain Energy ◽  
Long Span ◽  
Modal Coupling

Mode selection and modal coupling analysis are important to estimate wind-induced structural response of long-span roof structures. This article presents a framework for predicting wind-induced structural response of long-span roof structures based on modal analysis. This framework first identifies the dominant modes according to the correlation between the mode shape and the wind load spatial distribution on the structure as well as a proposed “modal participation coefficient.” Second, the concept of modal strain energy is introduced and a modal coupling coefficient is defined, based on which the dominant coupling modes are determined. A modified square root of the sum of the squares methodology is then developed to account for the modal coupling effects of the background and the resonant response components. The total responses can be obtained by combining the contributions of the dominant coupling modes and the square root of the sum of the squares results from the dominant modes. This avoids the use of the computation expensive complete quadratic combination method. Finally, an illustrative example of wind-induced response analysis of the China National Stadium roof structure is provided to demonstrate the effectiveness of the proposed framework.

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