Relevant bibliographies by topics / Sturm sequence

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

Academic literature on the topic 'Sturm sequence'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 April 2022

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Journal articles on the topic "Sturm sequence"

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Jo, Ji-Seong, Man-Gi Ko, Sang-Won Cho, and In-Won Lee. "Modified Sturm Sequence Property for Damped Systems." Journal of Engineering Mechanics 132, no. 7 (July 2006): 785–89. http://dx.doi.org/10.1061/(asce)0733-9399(2006)132:7(785).

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Evans, D. J. "Sturm sequence analysis of a diagonally bordered matrix." International Journal of Computer Mathematics 51, no. 1-2 (January 1994): 69–79. http://dx.doi.org/10.1080/00207169408804267.

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Fu, Hongguang, Lu Yang, and Zhenbing Zeng. "A recursive algorithm for constructing generalized Sturm sequence." Science in China Series E: Technological Sciences 43, no. 1 (December 2000): 32–41. http://dx.doi.org/10.1007/bf02917135.

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Cheng, Y. H., and C. K. Law. "On the quasi-nodal map for the Sturm–Liouville problem." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 136, no. 1 (February 2006): 71–86. http://dx.doi.org/10.1017/s0308210500004443.

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We show that the space of Sturm–Liouville operators characterized by H = (q, α, β) ∈ L1 (0, 1) × [0, π)2 such that is homeomorphic to the partition set of the space of all admissible sequences which form sequences that converge to q, α, and β individually. This space, Γ, of quasi-nodal sequences is a superset of, and is more natural than, the space of asymptotically nodal sequences defined in Law and Tsay (On the well-posedness of the inverse nodal problem. Inv. Probl.17 (2001), 1493–1512). The definition of Γ relies on the L1 convergence of the reconstruction formula for q by the exactly nodal sequence.
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Açil, M., and N. Bildik. "A SOLUTION TO INVERSE STURM-LIOUVILLE PROBLEMS." Advances in Mathematics: Scientific Journal 10, no. 9 (September 8, 2021): 3165–74. http://dx.doi.org/10.37418/amsj.10.9.6.

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In this study, we recover potential function and separable boundary conditions for the inverse Sturm-Liouville problem in normal form by using two partial subsets of the data which consist of its one spectrum and sequence of endpoints of eigenfunctions.
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Bunse-Gerstner, Angelika, and Chunyang He. "On a Sturm Sequence of Polynomials for Unitary Hessenberg Matrices." SIAM Journal on Matrix Analysis and Applications 16, no. 4 (October 1995): 1043–55. http://dx.doi.org/10.1137/s089547989223050x.

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Kashiwagi, Mitsuhiro, Itio Hirai, Takurou Katayama, and Walter D. Pilkey. "Sturm sequence recurrence formula for eigensolution of locally modified systems." Finite Elements in Analysis and Design 13, no. 1 (April 1993): 31–36. http://dx.doi.org/10.1016/0168-874x(93)90004-a.

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Shorter, Philip J. "On the use of the Sturm sequence to evaluate modal density." Journal of the Acoustical Society of America 108, no. 5 (November 2000): 2557. http://dx.doi.org/10.1121/1.4743493.

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Migda, Janusz, Magdalena Nockowska-Rosiak, and Małgorzata Migda. "Properties of Solutions of Generalized Sturm–Liouville Discrete Equations." Bulletin of the Malaysian Mathematical Sciences Society 44, no. 5 (March 19, 2021): 3111–27. http://dx.doi.org/10.1007/s40840-021-01105-y.

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AbstractWe consider discrete Sturm–Liouville-type equations of the form $$\begin{aligned} \varDelta (r_n\varDelta x_n)=a_nf(x_{\sigma (n)})+b_n. \end{aligned}$$ Δ ( r n Δ x n ) = a n f ( x σ ( n ) ) + b n . We present a theory of asymptotic properties of solutions which allows us to control the degree of approximation. Namely, we establish conditions under which for a given sequence y which solves the equation $$\varDelta (r_n\varDelta y_n)=b_n$$ Δ ( r n Δ y n ) = b n , the above equation possesses a solution x with the property $$x_n=y_n+\mathrm {o}(u_n)$$ x n = y n + o ( u n ) , where u is a given positive, nonincreasing sequence. The obtained results are applied to the study of asymptotically periodic solutions. Moreover, these results also allow us to obtain some nonoscillation criteria for the classical Sturm–Liouville equation.
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Chigansky, Pavel, and Marina Kleptsyna. "Sharp asymptotics in a fractional Sturm-Liouville problem." Fractional Calculus and Applied Analysis 24, no. 3 (June 1, 2021): 715–38. http://dx.doi.org/10.1515/fca-2021-0031.

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Abstract The current research of fractional Sturm-Liouville boundary value problems focuses on the qualitative theory and numerical methods, and much progress has been recently achieved in both directions. The objective of this paper is to explore a different route, namely, construction of explicit asymptotic approximations for the solutions. As a study case, we consider a problem with left and right Riemann-Liouville derivatives, for which our analysis yields asymptotically sharp estimates for the sequence of eigenvalues and eigenfunctions.
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Dissertations / Theses on the topic "Sturm sequence"

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NADER, Fabiano Neves. "Teorema de Sturm : uma demonstração detalhada do teorema de Sturm com propriedades e aplicações." Universidade Federal Rural de Pernambuco, 2014. http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/6704.

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Submitted by (lucia.rodrigues@ufrpe.br) on 2017-03-29T13:33:25Z No. of bitstreams: 1 Fabiano Neves Nader.pdf: 355299 bytes, checksum: 1b2a2621a49984f5afa2c5660f9b322a (MD5)
Made available in DSpace on 2017-03-29T13:33:25Z (GMT). No. of bitstreams: 1 Fabiano Neves Nader.pdf: 355299 bytes, checksum: 1b2a2621a49984f5afa2c5660f9b322a (MD5) Previous issue date: 2014-08-19
This study aims to build the entire theoretical basis for the understanding and use of the Sturm theorem, which is a tool very well grounded to find the number of real roots of a polynomial with real coefficients. During the development of this study sought to illustrate with examples and applications in great detail so that students and teachers are able to understand and use this beautiful algorithm.
Este trabalho tem por finalidade construir toda a base teórica para a compreensão e utilização do Teorema de Sturm, que é uma ferramenta muito bem fundamentada para encontrar a quantidade de raízes reais de um polinômio com coeficientes reais. Durante o desenvolvimento desse estudo procurei ilustrar com exemplos e aplicações de forma bem detalhada para que alunos e professores tenham condições de entender e utilizar este belíssimo algoritmo.
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Chan, Cy P. "Sturm sequences and the eigenvalue distribution of the beta-Hermite random matrix ensemble." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/40522.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.
Includes bibliographical references (p. 33).
This paper proposes that the study of Sturm sequences is invaluable in the numerical computation and theoretical derivation of eigenvalue distributions of random matrix ensembles. We first explore the use of Sturm sequences to efficiently compute histograms of eigenvalues for symmetric tridiagonal matrices and apply these ideas to random matrix ensembles such as the [beta]-Hermite ensemble. Using our techniques, we reduce the time to compute a histogram of the eigenvalues of such a matrix from O(n2 + m) to O(mn) time where n is the dimension of the matrix and m is the number of bins (with arbitrary bin centers and widths) desired in the histogram. Our algorithm is a significant improvement because m is usually much smaller than n. This algorithm allows us to compute histograms that were computationally infeasible before, such as those for n equal to 1 billion. Second, we give a derivation of the eigenvalue distribution for the [beta]-Hermite random matrix ensemble (for general [beta]). The novelty of the approach presented in this paper is in the use of Sturm sequences to derive the distribution. We derive an analytic formula in terms of multivariate integrals for the eigenvalue distribution and the largest eigenvalue distribution for general [beta] by analyzing the Sturm sequence of the tridiagonal matrix model. Finally, we explore the relationship between the Sturm sequence of a random matrix and its shooting eigenvectors. We show using Sturm sequences that, assuming the eigenvector contains no zeros, the number of sign changes in a shooting eigenvector of parameter A is equal to the number of eigenvalues greater than [lambda].
by Cy P. Chan.
S.M.
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Camargo-Brunetto, Maria Angelica de Oliveira. "Algoritmos algebricos para enumerar e isolar zeros polinomiais complexos." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 1994. http://hdl.handle.net/10183/25626.

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O presente trabalho trata do problema de isolar zeros de polinômios complexos. Muitos algoritmos calculam zeros polinomiais, a partir de regiões iniciais disjuntas, cada uma contendo um único zero. Entretanto o problema de obter tais regiões ainda e alvo de estudo, uma vez que as soluções propostas ainda não são satisfatórias. A obtenção de regiões disjuntas, denominada de isolamento de raízes está diretamente relacionada com a contagem (enumeração) do número de raízes numa determinada região do plano complexo. Algoritmos para enumerar e isolar raízes de polinômios complexos são analisados, desenvolvidos e implementados. A proposta de uma modificação no método numérico de Wilf e realizada, na qual se usa basicamente Seqüências de Sturm e o principio do argumento da analise complexa. Um enfoque algébrico e dado para o algoritmo, visando enumerar zeros de forma exata dentro de um retângulo. Diversas melhorias foram introduzidas, principalmente no tratamento da presença de zeros nas fronteiras de um retângulo alvo de pesquisa. O desempenho do algoritmo proposto e avaliado tanto nos aspectos teórico como pratico, através da determinação da complexidade teórica e através de testes experimentais. A abrangência do algoritmo também e verificada, através da realização de testes com polinômios mal condicionados. Uma comparação deste algoritmo com um recente trabalho e também realizada, mostrando a adequação deles de acordo com o tipo de polinômio.
In this thesis, the problem of isolating polynomial complex zeros is treated. There are many algorithms to calculate polynomial zeros, having previously isolated regions, each containning only one zero. Despite of this, the problem of obtainning such regions is still unsatisfactory. This problem, called root isolation, requires number of root in a given region of the complex plane. Algorithms to enumerate and isolate complex polynomial roots are analised, developed and implemented. A modified Wilf method is given, in with Sturm Sequences and the principle of argument is used. An algebraic approach is given, with the aim to enumerate zeros inside a rectangle in an exact way. Several improvements are introduced, mainly to treat zeros on the boundary of the rectangle. The performance of this new algorithm is evaluated theoretical as well as practice point of view, by means experimental tests. The robustness of the algorithm is verified by means of tests with ill-conditioned polynomials. The algorithm proposed is compared with a recent paper, presenting the performance of both, according different polynomial classes.
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Berglund, Filip. "Asymptotics of beta-Hermite Ensembles." Thesis, Linköpings universitet, Matematisk statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-171096.

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In this thesis we present results about some eigenvalue statistics of the beta-Hermite ensembles, both in the classical cases corresponding to beta = 1, 2, 4, that is the Gaussian orthogonal ensemble (consisting of real symmetric matrices), the Gaussian unitary ensemble (consisting of complex Hermitian matrices) and the Gaussian symplectic ensembles (consisting of quaternionic self-dual matrices) respectively. We also look at the less explored general beta-Hermite ensembles (consisting of real tridiagonal symmetric matrices). Specifically we look at the empirical distribution function and two different scalings of the largest eigenvalue. The results we present relating to these statistics are the convergence of the empirical distribution function to the semicircle law, the convergence of the scaled largest eigenvalue to the Tracy-Widom distributions, and with a different scaling, the convergence of the largest eigenvalue to 1. We also use simulations to illustrate these results. For the Gaussian unitary ensemble, we present an expression for its level density. To aid in understanding the Gaussian symplectic ensemble we present properties of the eigenvalues of quaternionic matrices. Finally, we prove a theorem about the symmetry of the order statistic of the eigenvalues of the beta-Hermite ensembles.
I denna kandidatuppsats presenterar vi resultat om några olika egenvärdens-statistikor från beta-Hermite ensemblerna, först i de klassiska fallen då beta = 1, 2, 4, det vill säga den gaussiska ortogonala ensemblen (bestående av reella symmetriska matriser), den gaussiska unitära ensemblen (bestående av komplexa hermitiska matriser) och den gaussiska symplektiska ensemblen (bestående av kvaternioniska själv-duala matriser). Vi tittar även på de mindre undersökta generella beta-Hermite ensemblerna (bestående av reella symmetriska tridiagonala matriser). Specifikt tittar vi på den empiriska fördelningsfunktionen och två olika normeringar av det största egenvärdet. De resultat vi presenterar för dessa statistikor är den empiriska fördelningsfunktionens konvergens mot halvcirkel-fördelningen, det normerade största egenvärdets konvergens mot Tracy-Widom fördelningen, och, med en annan normering, största egenvärdets konvergens mot 1. Vi illustrerar även dessa resultat med hjälp av simuleringar. För den gaussiska unitära ensemblen presenterar vi ett uttryck för dess nivåtäthet. För att underlätta förståelsen av den gaussiska symplektiska ensemblen presenterar vi egenskaper hos egenvärdena av kvaternioniska matriser. Slutligen bevisar vi en sats om symmetrin hos ordningsstatistikan av egenvärdena av beta-Hermite ensemblerna.
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Klopfenstein, Trey. "High-frequency Sequences within the Lower Mississippian Allensville Member, Logan Formation, South-central Ohio." Ohio University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1525864536290455.

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Shih, Cheng-Hau, and 石承浩. "On Sturm Sequence and Application." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/5qgun3.

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碩士
國立清華大學
數學系
93
Sturm theorem provides a classical method to lacate the roots of a real polynomial as well as the eigenvalues of a tridiagonal matrix. It exhibits an admirable simplicity in its proof and an easy manner in application. Various aspects of Sturm theorem are presented in this thesis. A partial answer is obtained to the initial object to find sufficint conditions for Sturm sequence.
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Books on the topic "Sturm sequence"

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McAdie, Colin. Effects of reduced resolution on the NEXRAD storm sequence algorithms. Boulder, Colo: U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, Environmental Research Laboratories, 1986.

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McAdie, Colin. Effects of reduced resolution on the NEXRAD storm sequence algorithms. Boulder, Colo: U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, Environmental Research Laboratories, 1986.

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Storm depositional systems: Dynamic stratigraphy in modern and ancient shallow-marine sequences. Berlin: Springer-Verlag, 1985.

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Wach, Grant D. Sedimentologyand sequence stratigraphy of a lower cretaceous tide and storm-dominated clastic succession, Isle of Wight and S.E. England. (Reading): British Sedimentological Research Group, 1991.

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Forecast Systems Laboratory (U.S.), ed. The performance of the NEXRAD storm sequence algorithms during a Colorado convective event. Boulder, Colo: U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, Environmental Research Laboratories, Forecast Systems Laboratory, 1995.

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Forecast Systems Laboratory (U.S.), ed. The performance of the NEXRAD storm sequence algorithms during a Colorado convective event. Boulder, Colo: U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, Environmental Research Laboratories, Forecast Systems Laboratory, 1995.

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Forecast Systems Laboratory (U.S.), ed. The performance of the NEXRAD storm sequence algorithms during a Colorado convective event. Boulder, Colo: U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, Environmental Research Laboratories, Forecast Systems Laboratory, 1995.

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Aigner, Thomas. Storm Depositional Systems: Dynamic Stratigraphy in Modern and Ancient Shallow-Marine Sequences (Lecture Notes in Earth Sciences). Springer, 1985.

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Quint, David. Reversing the Fall in Book 10. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161914.003.0008.

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This chapter places the reconciliation of Adam and Eve in book 10 against the preceding first two-thirds of book 10, which have described the building by Sin and Death of their bridge over Chaos and Satan's return to hell. Each of these appears to be a “triumphal act,” allusively associated with the triumph of Augustus depicted on the shield of Aeneas in Aeneid 8, the chronological “ending” of Virgil's poem. However, allusion equally returns both demonic acts to the beginning of the Aeneid, the storm and shipwreck off of Carthage, and suggests the recursive shape of evil in the larger book 10—a book in which the narrative sequence of events seems to run in a loop. Therefore, these satanic acts of heroism are now understood as mock-triumphs that parody the real triumphs of the Son—true endings that foreshadow apocalyptic ones—at the respective ends of books 6 and 7.
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Book chapters on the topic "Sturm sequence"

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Godunov, S. K., A. G. Antonov, O. P. Kiriljuk, and V. I. Kostin. "Sturm Sequences of Tridiagonal Matrices." In Guaranteed Accuracy in Numerical Linear Algebra, 313–423. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1952-8_4.

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Dam, G., and F. Surlyk. "Cyclic Sedimentation in a Large Wave- and Storm-Dominated Anoxic Lake; Kap Stewart Formation (Rhaetian-Sinemurian), Jameson Land, East Greenland." In Sequence Stratigraphy and Facies Associations, 417–48. Oxford, UK: Blackwell Publishing Ltd., 2009. http://dx.doi.org/10.1002/9781444304015.ch21.

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González-Vega, L., T. Recio, H. Lombardi, and M. F. Roy. "Sturm—Habicht Sequences, Determinants and Real Roots of Univariate Polynomials." In Texts and Monographs in Symbolic Computation, 300–316. Vienna: Springer Vienna, 1998. http://dx.doi.org/10.1007/978-3-7091-9459-1_14.

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Koskinen, Hannu E. J., and Emilia K. J. Kilpua. "Dynamics of the Electron Belts." In Astronomy and Astrophysics Library, 213–40. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-82167-8_7.

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AbstractIn this chapter we discuss the overall structure and dynamics of the electron belts and some of their peculiar features. We also consider the large-scale solar wind structures that drive geomagnetic storms and detail the specific responses of radiation belts on them. Numerous satellite observations have highlighted the strong variability of the outer electron belt and the slot region during the storms, and the energy and L-shell dependence of these variations. The belts can also experience great variations when interplanetary shocks or pressure pulses impact the Earth, even without a following storm sequence.
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Amorocho, Jaime, and Baolin Wu. "Mathematical Models for the Simulation of Cyclonic Storm Sequences and Precipitation Fields." In Precipitation Analysis for Hydrologic Modeling, 210–25. Washington, D. C.: American Geophysical Union, 2013. http://dx.doi.org/10.1029/sp004p0210.

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Adam, John A. "Introduction." In Rays, Waves, and Scattering. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691148373.003.0001.

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This book deals with rays, waves, and scattering and covers many of the mathematical concepts, structures, and techniques used to study them. The subject of rays is explored in an atmosphere–sea–earth sequence, while waves are examined via the reverse sequence earth–sea–atmosphere. The book also considers the relationship between the elegance of the classical Lagrangian and Hamiltonian formulations of mechanics and optics; Kepler's laws of planetary motion, developed from gravitational scattering; surface gravity waves; diffraction; acoustics; electromagnetic scattering, including the Mie solution; and the WKB(J) approximation and its application to some simple one-dimensional potentials. The book concludes with an analysis of the salient properties of Sturm-Liouville systems with particular reference to the time-independent Schrödinger equation. This chapter provides an overview of the rainbow directory, rays, waves, classical and semiclassical scattering, and caustics and diffraction catastrophes.
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"Sturm Sequences and Greatest Common Divisors." In Studies in Computational Mathematics, 37–52. Elsevier, 2007. http://dx.doi.org/10.1016/s1570-579x(07)80005-x.

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Hook, D. G., and P. R. McAree. "USING STURM SEQUENCES TO BRACKET REAL ROOTS OF POLYNOMIAL EQUATIONS." In Graphics Gems, 416–22. Elsevier, 1990. http://dx.doi.org/10.1016/b978-0-08-050753-8.50089-9.

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NIEDORODA, ALAN WILLIAM, DONALD J. P. SWIFT, and JULIANA THORNE. "MODELING SHELF STORM BEDS: CONTROLS OF BED THICKNESS AND BEDDING SEQUENCE." In Shelf Sedimentation, Shelf Sequences and Related Hydrocarbon Accumulation. SEPM Society for Sedimentary Geology, 1989. http://dx.doi.org/10.5724/gcs.89.07.0015.

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Brackett, Robert S., and David M. Bush. "SEDIMENTARY CHARACTERISTICS OF MODERN STORM-GENERATED SEQUENCES: NORTH INSULAR SHELF, PUERTO RICO." In Modern and Ancient Shelf Clastics, 125–68. SEPM (Society for Sedimentary Geology), 1986. http://dx.doi.org/10.2110/cor.86.01.0125.

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Conference papers on the topic "Sturm sequence"

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Gaonzalez, L., H. Lombardi, T. Recio, and M. F. Roy. "Sturm-Habicht sequence." In the ACM-SIGSAM 1989 international symposium. New York, New York, USA: ACM Press, 1989. http://dx.doi.org/10.1145/74540.74558.

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Hashemi, S. M., M. J. Richard, and G. Dhatt. "A Bernoulli-Euler Stiffness Matrix Approach for Vibrational Analysis of Spinning Linearly Tapered Beams." In ASME 1997 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/97-gt-500.

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This paper presents a Dynamic Finite Element (DFE) formulation, based on the Dynamic Stiffness Matrix (DSM) approach, for vibrational analysis of spinning beams. The constituent members are considered to be linearly tapered as well as centrifugally stiffened. A non-dimensional formulation is considered, and the frequency dependent trigonometric shape functions are used to find a single frequency dependent element matrix (called DSM) which has both mass and stiffness properties. An adapted bisection method based on a Sturm sequence root counting technique, is used to find the first four out-of-plane flexural natural frequencies of a cantilevered linearly tapered (in height) beam for different non-dimensional rotating speeds. The results have been compared to those found by finite elements method using Hermite beam elements. Much better convergency rates are found by this method when comparing to conventional finite element methods.
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Hashemi, Seyed M. "Vibration Analysis of Axially Loaded Beams Including Rotary Inertia: An Exact Dynamic Finite Element." In ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/detc2004-57789.

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An ‘exact’ basis function Dynamic Finite Element (DFE) for the free vibrational analysis of axially loaded beams and assemblages composed of beams is presented. The shear deformation is neglected but the Rotary Inertia (RI) effects are taken into consideration. The dynamic trigonometric shape functions for bending vibrations of an axially loaded uniform beam element are first derived in an exact sense. Then, exploiting the Principle of Virtual Work together with the nodal approximations of variables based on these dynamic shape functions, leads to a single frequency dependent Dynamic Stiffness Matrix (DSM) that represents both mass and stiffness properties. A Wittrick-Williams algorithm, based on a Sturm sequence root counting technique, is then used as the solution method. The application of the theory is demonstrated by an illustrative example of cantilever beam where the influence of Rotary Inertia (RI) effect and different axial loads on the natural frequencies of the system is demonstrated by numerical results.
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Hashemi, S. M., and M. J. Richard. "On the Natural Frequency Calculation of Rotating Cantilever Uniform Beams With Coriolis Effects: A Dynamic Finite Element (DFE)." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8269.

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Abstract A Dynamic Finite Element (DFE) for vibrational analysis of rotating assemblages composed of beams is presented in which the complexity of the acceleration, due to the presence of gyroscopic, or Coriolis forces, is taken into consideration. The dynamic trigonometric shape functions of uncoupled bending and axial vibrations of an axially loaded uniform beam element are derived in an exact sense. Then, exploiting the Principle of Virtual Work together with the nodal approximations of variables, based on these dynamic shape functions, leads to a single frequency dependent stiffness matrix which is Hermitian and represents both mass and stiffness properties. A Wittrick-Williams algorithm, based on a Sturm sequence root counting technique, is then used as the solution method. The application of the theory is demonstrated by two illustrative examples of vertical and radial beams where the influence of Coriolis forces on natural frequencies of the clamped-free rotating beams is demonstrated by numerical results.
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Bachynski, Erin E., Ana Page, and George Katsikogiannis. "Dynamic Response of a Large-Diameter Monopile Considering 35-Hour Storm Conditions." In ASME 2019 38th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/omae2019-95170.

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Abstract As a part of the assessment of foundation resistance for monopiles, several offshore wind standards prescribe symmetric 35-hour (or 42-hour) storm sequences in terms of wind speed and significant wave height. The temporal evolution of the peak period is not specified explicitly in the standards, despite the fact that large monopile wind turbines are sensitive to the wave period. In the present work, the storm sequences according to the standards are first compared to hindcast data for intermediate water depth locations in the North Sea. An alternative storm sequence is proposed based on the hindcast data, and possible values of the peak period evolution are proposed for the standard models. The responses of a 10 MW monopile wind turbine are then computed for both the standard and proposed sequences using a time domain aero-hydro-servo-elastic code coupled to a macro element model for the soil-structure interaction. The resulting mudline load cycles are then compared for the different storm sequences.
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Laface, Valentina, Anne Karin Magnusson, Elzbieta M. Bitner-Gregersen, Magnar Reistad, Alessandra Romolo, and Felice Arena. "Equivalent Storm Model for Long-Term Statistics of Sea Storms Off Norway." In ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/omae2018-78747.

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The paper deals with long-term analysis of ocean storms off Norway. Sixty years of wave model time series are considered for the analysis. The input data provide spectral characteristics of both wind and swell seas. The availability of global and partitioned significant wave heights enables the possibility of investigating how swell seas influence the storm shape in terms of growing and decay stages and on how this aspect affects the long-term estimates. The analysis is conducted by means of equivalent storm approach which consists of substituting the sequence of actual storms at a given site with a sequence of equivalent storms whose shape is fixed (such as triangular, power or exponential) and then calculating return periods of storm with given characteristics via analytical solutions derived on the basis of storm shape assumed. This is possible due to statistical equivalence between actual and equivalent storms which in turn leads to the equality of wave risk between actual and equivalent storm sequences at a given site. The equivalent storm associated with an actual one is defined by means of two parameters, related to the storm intensity and duration. The equivalent storm intensity is given by the maximum significant wave height in the actual storm history, while the duration is determined via an iterative procedure. In this paper the exponential shape is considered which is referred as equivalent exponential (EES) storm model. Some aspects related with the storm shape and its influence on return values estimate via EES model are investigated. Further, a sensitivity analysis of EES model to the storm threshold is proposed.
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7

Rijken, Oriol, and Adam Bangs. "Wave Measurements at Eastern Green Canyon During Hurricane Ike." In ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2009. http://dx.doi.org/10.1115/omae2009-79802.

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Wave measurements were obtained at an Eastern Green Canyon location during hurricane Ike in September 2009. The eye of the hurricane passed approximately 68 nautical miles to the South West of the measurement location. The significant wave height was above 30 ft for about 20 hours and above 40 ft for about 5.5 hours. The wave time series provide an insight into the wave field as the storm approaches and leaves the location. One of the interesting features observed was that there were repetitive sequences, where each sequence consisted of a period of increased wave energy followed by periods of reduced wave energy. Each sequence lasted approximately one hour. Measured wave crest, wave trough and wave height distributions are discussed. One unique wave event was observed. This event was characterized by a predictably-sized crest followed by a very deep trough.
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8

De Gracia, Luis, Naoki Osawa, Wengang Mao, and Daichi Ichihashi. "Influence of Different Wave Load Sequence Models on Fatigue Life Prediction of Ship Structures Based on Fracture Mechanics Approach." In ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/omae2016-54688.

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FCP (Fatigue Crack Propagation) based fatigue assessments of a welded joint in a 2800 TEU container ship which sails on North Atlantic routes are performed. The Great-circle course with small variation of relative heading angle and a southerly course with large variation of relative heading angle are considered. Short sea sequences are generated by using ‘storm model’ developed by Osaka University and ‘spatio-temporal model’ developed by Chalmers University. Sea keeping analyses are performed for both cases wherein the variation in wave direction’s occurrence probability is considered (‘real headings model’) and not (‘all-headings model’). FCP analyses are performed considering plasticity-induced crack closure by using FASTRAN-II. Fatigue crack propagation lives and characteristics of crack propagation retardation due to excessive loads are compared. Based these results, the influence of the difference in load sequence model on FCP-based fatigue assessment result is discussed.
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9

Long, D. G. "Finding the global minima of objective functions using modified Sturm sequences." In [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing. IEEE, 1991. http://dx.doi.org/10.1109/icassp.1991.150579.

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Laface, Valentina, Felice Arena, Christophe Maisondieu, and Alessandra Romolo. "On Long Term Statistics of Ocean Storms Starting From Partitioned Sea States." In ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/omae2017-61750.

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The paper proposes an analysis of ocean storms carried out starting from significant wave height time series of HOMERE sea-states hindcast database based on WAVEWATCH III model. Considering that wave spectra often exhibit multiple peaks due to the coexistence of wind waves and swells, here sea states are described by partitioned sea states that can be interpreted physically as representing independent wave systems. The analysis presented here in the paper deals with the contribution of swells to the storm peaks and on how they influence the long term statistics. The sensitivity of return values of significant wave height to swell contribution is investigated via an application of the Equivalent Triangular Storm Model (ETS). The ETS model provides analytical solution for the calculation of the return period R(Hs>h) of a sea storm whose maximum significant wave height exceeds a given threshold h. The approach of ETS consists in substituting each actual storm with an ETS described by two parameters: the storm intensity, that is the triangle height and it is equal to the maximum significant wave height during the actual storm; the storm duration, that is achieved imposing the equality between the maximum expected wave height of actual and equivalent storms. It has been experimentally proved that the actual storm and associated ETS are statistically equivalent because they have the same maximum significant wave height and the same probability P(Hmax>H) that the maximum wave height exceeds a given threshold H. The sequence of ETSs obtained in this way represents the equivalent sea, while the sequence of actual storms is the actual sea. The equivalent and actual seas present the same wave risk because they are characterized by the same number of storm events, each of them with the same intensity and the same P(Hmax>H). For the proposed analysis a set of four points from open sea to the coast is considered in area of the Gulf of Biscay (France). The results show that the contribution of swells is more significant for the storms of small and medium intensity and decreases for increasing storm intensities. Further return values variability neglecting swell is less than 7% at any point for return periods up to 100 years.
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