Relevant bibliographies by topics / Fourier-sine series

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Fourier-sine series'

Author: Grafiati
Published: 4 June 2021
Last updated: 19 February 2022

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Journal articles on the topic "Fourier-sine series"

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Glasser, M. L., and H. E. Fettis. "A Fourier Sine Series." SIAM Review 28, no. 2 (June 1986): 233. http://dx.doi.org/10.1137/1028058.

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Oganesyan, K. A. "Generalized Double Fourier Sine Series." Moscow University Mathematics Bulletin 73, no. 1 (January 2018): 9–16. http://dx.doi.org/10.3103/s0027132218010023.

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Mekonen, Belete Debalkie, and Getachew Abiye Salilew. "Geometric Series on Fourier Cosine-Sine Transform." Journal of Advances in Mathematics and Computer Science 28, no. 4 (September 1, 2018): 1–4. http://dx.doi.org/10.9734/jamcs/2018/42892.

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PAN, XUEZAI, MINGGANG WANG, and XUDONG SHANG. "FOURIER SERIES REPRESENTATION OF FRACTAL INTERPOLATION FUNCTION." Fractals 28, no. 04 (May 22, 2020): 2050063. http://dx.doi.org/10.1142/s0218348x20500632.

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The purpose of this research is to show how the complicated and irregular fractal interpolation function is represented by Fourier series. First, on the closed interval [0,1], even prolongation is operated to the fractal interpolation function generated by iterated function system constituted by affine transform and Fourier cosine series representation of fractal interpolation function is proved. Second, for fractal interpolation function, odd prolongation is done and Fourier sine series formula of fractal interpolation function is proved. Final, Fourier series expansion of fractal interpolation function on the closed interval [Formula: see text] is proved. The result shows that complex fractal interpolation function can be represented by Fourier sine series and Fourier cosine series, so relatively simple Fourier series can be used to represent relatively complicated fractal interpolation function.
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Tomovski, Zivorad. "New integral and series representations of the generalized Mathieu series." Applicable Analysis and Discrete Mathematics 2, no. 2 (2008): 205–12. http://dx.doi.org/10.2298/aadm0802205t.

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By using some recently investigated fourier sine integral representations for the Mathieu type series (see [4]), new integral and series representations are derived here for certain general families of Mathieu type series.
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Petros, Biruk. "Navier-Stokes Three Dimensional Equations Solutions Volume Three." Journal of Mathematics Research 10, no. 4 (July 25, 2018): 128. http://dx.doi.org/10.5539/jmr.v10n4p128.

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Solution of Navier-Stokes equation is found by introducing new method for solving differential equations. This new method is writing periodic scalar function in any dimensions and any dimensional vector fields as the sum of sine and cosine series with proper coefficients. The method is extension of Fourier series representation for one variable function to multi-variable functions and vector fields.Before solving Navier-Stokes equations we introduce a new technique for writing periodic scalar functions or vector fields as the sum of cosine and sine series with proper coefficients. Fourier series representation is background for our new technique.Periodic nature of initial velocity for Navier-Stokes problem helps us write the vector field in the form of cosine and sine series sum which simplify the problem.
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SHIOGAI, Kazuki, Naoto SASAOKA, Masaki KOBAYASHI, Isao NAKANISHI, James OKELLO, and Yoshio ITOH. "Bias Free Adaptive Notch Filter Based on Fourier Sine Series." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E97.A, no. 2 (2014): 557–64. http://dx.doi.org/10.1587/transfun.e97.a.557.

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Osborne, Alfred R. "Nonlinear Fourier Analysis: Rogue Waves in Numerical Modeling and Data Analysis." Journal of Marine Science and Engineering 8, no. 12 (December 9, 2020): 1005. http://dx.doi.org/10.3390/jmse8121005.

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Nonlinear Fourier Analysis (NLFA) as developed herein begins with the nonlinear Schrödinger equation in two-space and one-time dimensions (the 2+1 NLS equation). The integrability of the simpler nonlinear Schrödinger equation in one-space and one-time dimensions (1+1 NLS) is an important tool in this analysis. We demonstrate that small-time asymptotic spectral solutions of the 2+1 NLS equation can be constructed as the nonlinear superposition of many 1+1 NLS equations, each corresponding to a particular radial direction in the directional spectrum of the waves. The radial 1+1 NLS equations interact nonlinearly with one another. We determine practical asymptotic spectral solutions of the 2+1 NLS equation that are formed from the ratio of two phase-lagged Riemann theta functions: Surprisingly this construction can be written in terms of generalizations of periodic Fourier series called (1) quasiperiodic Fourier (QPF) series and (2) almost periodic Fourier (APF) series (with appropriate limits in space and time). To simplify the discourse with regard to QPF and APF Fourier series, we call them NLF series herein. The NLF series are the solutions or approximate solutions of the nonlinear dynamics of water waves. These series are indistinguishable in many ways from the linear superposition of sine waves introduced theoretically by Paley and Weiner, and exploited experimentally and theoretically by Barber and Longuet-Higgins assuming random phases. Generally speaking NLF series do not have random phases, but instead employ phase locking. We construct the asymptotic NLF series spectral solutions of 2+1 NLS as a linear superposition of sine waves, with particular amplitudes, frequencies and phases. Because of the phase locking the NLF basis functions consist not only of sine waves, but also of Stokes waves, breather trains, and superbreathers, all of which undergo complex pair-wise nonlinear interactions. Breather trains are known to be associated with rogue waves in solutions of nonlinear wave equations. It is remarkable that complex nonlinear dynamics can be represented as a generalized, linear superposition of sine waves. NLF series that solve nonlinear wave equations offer a significant advantage over traditional periodic Fourier series. We show how NLFA can be applied to numerically model nonlinear wave motions and to analyze experimentally measured wave data. Applications to the analysis of SINTEF wave tank data, measurements from Currituck Sound, North Carolina and to shipboard radar data taken by the U. S. Navy are discussed. The ubiquitous presence of coherent breather packets in many data sets, as analyzed by NLFA methods, has recently led to the discovery of breather turbulence in the ocean: In this case, nonlinear Fourier components occur as strongly interacting, phase locked, densely packed breather modes, in contrast to the previously held incorrect belief that ocean waves are weakly interacting sine waves.
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Sholiha, Anisatus, Kuzairi Kuzairi, and M. Fariz Fadillah Madianto. "Estimator Deret Fourier Dalam Regresi Nonparametrik dengan Pembobot Untuk Perencanaan Penjualan Camilan Khas Madura." Zeta - Math Journal 4, no. 1 (May 16, 2018): 18–23. http://dx.doi.org/10.31102/zeta.2018.4.1.18-23.

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The purpose of regression analysis is determining the relationship between response variables to predictor variables. To estimate the regression curve there are three approaches, parametric regression, nonparametric regression, and semiparametric regression. In this study, the estimator form of nonparametric regression curve is analyzed by using the Fourier series approach with sine and cosine bases, sine bases, and cosine bases. Based on Weighted Least Square (WLS) optimization, the estimator result can be applied to model the sale planning of Madura typical snacks. Nonparametric regression estimators with the Fourier series approach are weighted with uniform and variance weight. The best model that be obtained in this study for uniform weight, based on cosine and sine basis with GCV value ​​of 1541.015, MSE value of 0.1375912 and determination coefficient value of 0.4728418%. The best model for variance weight is based on cosine and sine basis with a GCV value of 1541.011, MSE value of 0.1375912 and determination coefficient of 0.4728227%.
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Jagers, A. A. "A Fourier Sine Series (M. L. Glasser and H. E. Fettis)." SIAM Review 29, no. 2 (June 1987): 303–5. http://dx.doi.org/10.1137/1029054.

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Dissertations / Theses on the topic "Fourier-sine series"

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Linder, Olivia. "Solving an inverse problem for an elliptic equation using a Fourier-sine series." Thesis, Linköpings universitet, Matematiska institutionen, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-162371.

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This work is about solving an inverse problem for an elliptic equation. An inverse problem is often ill-posed, which means that a small measurement error in data can yield a vigorously perturbed solution. Regularization is a way to make an ill-posed problem well-posed and thus solvable. Two important tools to determine if a problem is well-posed or not are norms and convergence. With help from these concepts, the error of the reg- ularized function can be calculated. The error between this function and the exact function is depending on two error terms. By solving the problem with an elliptic equation, a linear operator is eval- uated. This operator maps a given function to another function, which both can be found in the solution of the problem with an elliptic equation. This opera- tor can be seen as a mapping from the given function’s Fourier-sine coefficients onto the other function’s Fourier-sine coefficients, since these functions are com- pletely determined by their Fourier-sine series. The regularization method in this thesis, uses a chosen number of Fourier-sine coefficients of the function, and the rest are set to zero. This regularization method is first illustrated for a simpler problem with Laplace’s equation, which can be solved analytically and thereby an explicit parameter choice rule can be given. The goal with this work is to show that the considered method is a reg- ularization of a linear operator, that is evaluated when the problem with an elliptic equation is solved. In the tests in Chapter 3 and 4, the ill-posedness of the inverse problem is illustrated and that the method does behave like a regularization is shown. Also in the tests, it can be seen how many Fourier-sine coefficients that should be considered in the regularization in different cases, to make a good approximation.
Det här arbetet handlar om att lösa ett inverst problem för en elliptisk ekvation. Ett inverst problem är ofta illaställt, vilket betyder att ett litet mätfel i data kan ge en kraftigt förändrad lösning. Regularisering är ett tillvägagångssätt för att göra ett illaställt problem välställt och således lösbart. Två viktiga verktyg för att bestämma om ett problem är välställt eller inte är normer och konvergens. Med hjälp av dessa begrepp kan felet av den regulariserade lösningen beräknas. Felet mellan den lösningen och den exakta är beroende av två feltermer. Genom att lösa problemet med den elliptiska ekvationen, så är en linjär operator evaluerad. Denna operator avbildar en given funktion på en annan funktion, vilka båda kan hittas i lösningen till problemet med en elliptisk ekva- tion. Denna operator kan ses som en avbildning från den givna funktions Fouri- ersinuskoefficienter på den andra funktionens Fouriersinuskoefficienter, eftersom dessa funktioner är fullständigt bestämda av sina Fouriersinusserier. Regularise- ringsmetoden i denna rapport använder ett valt antal Fouriersinuskoefficienter av funktionen, och resten sätts till noll. Denna regulariseringsmetod illustreras först för ett enklare problem med Laplaces ekvation, som kan lösas analytiskt och därmed kan en explicit parametervalsregel anges. Målet med detta arbete är att visa att denna metod är en regularisering av den linjära operator som evalueras när problemet med en elliptisk ekvation löses. I testerna i kapitel 3 och 4, illustreras illaställdheten av det inversa problemet och det visas att metoden beter sig som en regularisering. I testerna kan det också ses hur många Fouriersinuskoefficienter som borde betraktas i regulariseringen i olika fall, för att göra en bra approximation.
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Book chapters on the topic "Fourier-sine series"

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Orsingher, E. "On the Maximum of Gaussian Fourier Sine Series Connected with Random Vibrations." In Biomathematics and Related Computational Problems, 555–58. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2975-3_49.

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"Fourier Series over Finite Intervals (Sine and Cosine Series)." In Principles of Fourier Analysis, 135–42. CRC Press, 2001. http://dx.doi.org/10.1201/9781420036909-13.

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Liengme, Bernard V. "Superposition of sine waves and Fourier series." In Modelling Physics with Microsoft Excel. Morgan & Claypool Publishers, 2014. http://dx.doi.org/10.1088/978-1-627-05419-5ch7.

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"Fourier Series over Finite Intervals (Sine and Cosine Series)." In Textbooks in Mathematics, 121–28. CRC Press, 2001. http://dx.doi.org/10.1201/9781420036909.ch10.

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Glusker, Jenny Pickworth, and Kenneth N. Trueblood. "The phase problem and electron-density maps." In Crystal Structure Analysis. Oxford University Press, 2010. http://dx.doi.org/10.1093/oso/9780199576340.003.0015.

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In order to obtain an image of the material that has scattered X rays and given a diffraction pattern, which is the aim of these studies, one must perform a three-dimensional Fourier summation. The theorem of Jean Baptiste Joseph Fourier, a French mathematician and physicist, states that a continuous, periodic function can be represented by the summation of cosine and sine terms (Fourier, 1822). Such a set of terms, described as a Fourier series, can be used in diffraction analysis because the electron density in a crystal is a periodic distribution of scattering matter formed by the regular packing of approximately identical unit cells. The Fourier series that is used provides an equation that describes the electron density in the crystal under study. Each atom contains electrons; the higher its atomic number the greater the number of electrons in its nucleus, and therefore the higher its peak in an electrondensity map.We showed in Chapter 5 how a structure factor amplitude, |F (hkl)|, the measurable quantity in the X-ray diffraction pattern, can be determined if the arrangement of atoms in the crystal structure is known (Sommerfeld, 1921). Now we will show how we can calculate the electron density in a crystal structure if data on the structure factors, including their relative phase angles, are available. The Fourier series is described as a “synthesis” when it involves structure amplitudes and relative phases and builds up a picture of the electron density in the crystal. By contrast, a “Fourier analysis” leads to the components that make up this series. The term “relative” is used here because the phase of a Bragg reflection is described relative to that of an imaginary wave diffracted in the same direction at a chosen origin of the unit cell.
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Conference papers on the topic "Fourier-sine series"

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Hague, David A. "Nonlinear frequency modulation using fourier sine series." In 2018 IEEE Radar Conference (RadarConf18). IEEE, 2018. http://dx.doi.org/10.1109/radar.2018.8378700.

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Osborne, Alfred R. "Theory of Nonlinear Fourier Analysis: The Construction of Quasiperiodic Fourier Series for Nonlinear Wave Motion." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-18850.

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Abstract I give a description of nonlinear water wave dynamics using a recently discovered tool of mathematical physics I call nonlinear Fourier analysis (NLFA). This method is based upon and is an application of a theorem due to Baker [1897, 1907] and Mumford [1984] in the field of algebraic geometry and from additional sources by the author [Osborne, 2010, 2018, 2019]. The theory begins with the Kadomtsev-Petviashvili (KP) equation, a two dimensional generalization of the Korteweg-deVries (KdV) equation: Here the NLFA method is derived from the complete integrability of the equation by finite gap theory or the inverse scattering transform for periodic/quasiperiodic boundary conditions. I first show, for a one-dimensional, plane wave solution, that the KP equation can be rotated to a solution of the KdV equation, where the coefficients of KdV are now functions of the rotation angle. I then show how the rotated KdV equation can be used to compute the spectral solutions of the KP equation itself. Finally, I write the spectral solutions of the KP equation as a finite gap solution in terms of Riemann theta functions. By virtue of the fact that I am able to write a theta function formulation of the KP equation, it is clear that the wave dynamics lie on tori and constitute parallel dynamics on the tori in the integrable cases and non-parallel dynamics on the tori for certain perturbed quasi-integrable cases. Therefore, we are dealing with a Kolmogorov-Arnold-Moser KAM theory for nonlinear partial differential wave equations. The nonlinear Fourier series have particular nonlinear Fourier modes, including: sine waves, Stokes waves and solitons. Indeed the theoretical formulation I have developed is a kind of exact two-dimensional “coherent wave turbulence” or “integrable wave turbulence” for the KP equation, for which the Stokes waves and solitons are the coherent structures. I discuss how NLFA provides a number of new tools that apply to a wide range of problems in offshore engineering and coastal dynamics: This includes nonlinear Fourier space and time series analysis, nonlinear Fourier wave field analysis, a nonlinear random phase approximation, the study of nonlinear coherent functions and nonlinear bi and tri spectral analysis.
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Malookani, Rajab A., and Wim T. van Horssen. "On the Vibrations of an Axially Moving String With a Time-Dependent Velocity." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-50452.

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The transverse vibrations of an axially moving string with a time-varying speed is studied in this paper. The governing equations of motion describing an axially moving string is analyzed using two different techniques. At first, the initial-boundary value problem is discretized using the Fourier sine series, and then the two timescales perturbation method is employed in search of infinite mode approximate solutions. Secondly, a new approach based on the two timescales perturbation method and the method of characteristics is used. It is found that there are infinitely many values of the velocity fluctuation frequency yielding infinitely many resonance conditions in the system. The response of the system with harmonically varying velocity function is computed for particular harmonic initial conditions.
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Kim, Hyeong Koo, Jae Ik Kim, Kyu Tae Kim, and Moon Saeng Kim. "Frequency Equations for Vibration Analysis of Fuel Rod." In ASME 2005 Pressure Vessels and Piping Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/pvp2005-71162.

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In this study, the frequency equations for calculating the natural frequencies of the beams with generally restrained boundary conditions by both translational and rotational springs are derived in matrix form using Fourier sine series. In order to show the validation of the solution, numerical results for two degenerate cases are compared with existing results for natural frequency obtained by the conventional analysis. And as a specific application, the natural frequencies of fuel rod for KSNP (Korean Standard Nuclear Plant) fuel assembly are calculated and compared with the external excitations. As a result, the frequency equation derived by present paper seems to be very useful to evaluate the natural frequencies of the double span beams with various boundary conditions. Especially, when some parametric analyses are needed to modify fuel design, the equation can be applied very easily.
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Sakagami, Takahide, and Shiro Kubo. "Development of Lock-In Infrared Thermography Techniques for Quantitative Nondestructive Evaluations." In ASME 2007 Pressure Vessels and Piping Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/pvp2007-26788.

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In this paper, lock-in thermography techniques for quantitative nondestructive evaluations developed by the present authors are reviewed. Self-reference lock-in thermography was developed for remote nondestructive testing of fatigue cracks. This technique is based on the measurement of thermoelastic temperature change due to stress change. Cracks can be identified from significant temperature change observed at crack tips due to the stress singularity. For accurate measurement of the thermoelastic temperature change under random loading, a self-reference lock-in data processing technique was developed, in which a reference signal was constructed by using the temperature data simultaneously taken at a remote area. Thermoelastic temperature change in a region of interest was correlated with that at the area for reference signal construction. It enabled us to measure the relative stress distribution under random loading without using any external loading signal. The self-reference lock-in thermography was applied for fatigue crack identification in welded steel plate specimens and actual steel structures. It was found that significant temperature change was observed at the crack tip in the self-reference lock-in thermal image, demonstrating the feasibility of the proposed technique. Lock-in thermography technique was also applied to quantitative nondestructive evaluation of material loss defects. Transient temperature data under pulse or step heating were measured by infrared thermography. Temperature data were processed by the lock-in analysis scheme based on the Fourier series expansion, in which Fourier coefficients synchronizing with sine and cosine waves were correlated with defect parameters. Experimental investigations were conducted using steel samples with artificial material loss defects. It was found that the defect parameters can be quantitatively determined from the Fourier coefficients, demonstrating the feasibility of the proposed technique.
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Osborne, Alfred R. "Advances in Nonlinear Waves With Emphasis on Aspects for Ship Design and Wave Forensics." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-10873.

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Prof. D. Faulkner emphasized the importance of the study of extreme/rogue waves when he noted that the use of sine waves for computing pressures in the design of ships was no longer tenable, primarily because of the large number of cases where extreme structural damage has been encountered due to highly nonlinear large waves. This perspective resulted in the creation of the European program MaxWave and the subsequent program Extreme Seas soon followed. Recently my own studies of nonlinear effects in water waves at Nonlinear Waves Research Corporation (NWRC) have resulted in a number of successes with regard to the fundamental physical understanding of rogue waves. These studies enlarge our ability to understand the requisite impact of extreme waves on the design of ships. Some of these advances are: (1) The determination of analytical techniques for describing rogue wave packets in two dimensions for random sea states which are directionally spread. (2) The description of wave overturning and breaking in directional sea states with the Type II (lateral) instability. (3) The development of hyperfast computer models for the deterministic simulation of directional sea states. (4) The development of a fast approach for computing the full Boltzmann integral (FBI) for the nonlinear wave/wave interactions in wind/wave models. (5) The identification of the actual physical location in the power spectrum for the nonlinear Fourier rogue wave components. (6) The development of nonlinear Fourier techniques for analyzing times series of ocean waves for the presence of rogue wave states. (7) The development of fully nonlinear directional spectra (in terms of frequency and direction) from arrays of instruments. (8) The development of hindcasting and predicting capability for the assessment of the onset of a rogue sea. I also discuss a number of future developments now underway at NWRC.
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Sigrist, Jean Franc¸ois, Christian Laine, and Bernard Peseux. "Dynamic Analysis of a Coupled Fluid Structure Problem With Fluid Sloshing." In ASME/JSME 2004 Pressure Vessels and Piping Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/pvp2004-3043.

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The present paper is related to the study of a generic linear coupled fluid/structure problem, in which an elastic beam is coupled with an inviscid fluid, with or without sloshing effects. A previous study [18] focussed on added mass effects; the present study is devoted to the coupling effects between fluid sloshing modes and structure with fluid added mass modes. The discretization of the coupled linear equations is performed with an axisymmetric fluid pressure formulated element, expanded in terms of a FOURIER series [14]. Various linear fluid model are taken into account (compressible, uncompressible, with or without sloshing) with the corresponding coupling matrix operator. The modal analysis is performed with a MATLAB program, using the non-symmetric LANCZOS algorithm [16]. The temporal analysis is performed with classical numerical techniques [10], in order to describe the dynamic response of the coupled problem subjected to a simple sine wave shock. The coupling effects are studied in various conditions represented by several non-dimensionnal numbers [12] such as the dynamic FROUDE number and the mass number, based on the geometrical and physical characteristics of the coupled problem. Comparisons are performed on the coupled problem with or without free surface modeling, with a model and temporal analysis. Coupling effects are exhibited and quantified; the numerical results obtained in the modal analysis here are in good agreement with other previous studies, carried out on different geometry [3,15]. The temporal analysis gives another point of view on the importance of the coupling effects and their importance at low dynamic FROUDE numbers. The present study gives and will be completed with a non-linear analysis (for both fluid and structure problems) of the coupled problem, using a finite element and finite volume explicit coupling procedure [19].
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