Academic literature on the topic 'Generalized complex Lamé coefficients'
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Journal articles on the topic "Generalized complex Lamé coefficients"
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Joshi, Nalini, and Andrew Pickering. "Generalized Halphen systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 136, no. 6 (December 2006): 1287–301. http://dx.doi.org/10.1017/s0308210500004984.
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Towards the end of the nineteenth century, Halphen studied a remarkable sequence of higher-order linear equations with doubly periodic coefficients, generalizations of a certain Lamé equation, having the property that quotients of solutions are single valued. Here we consider further generalizations where, instead of the Weierstrass ℘-function, the coefficients depend on the first Painlevé transcendent. Using these equations, we obtain new higher-order systems of nonlinear equations having the Painlevé property. We also give new results on the interpretation of the Painlevé tests with regard to the representations of solutions, general and particular, afforded by various branches, and to understanding the corresponding pattern of compatibility conditions.
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Khomasuridze, N. "Representation of Solutions of Some Boundary Value Problems of Elasticity by a Sum of the Solutions of Other Boundary Value Problems." gmj 10, no. 2 (June 2003): 257–70. http://dx.doi.org/10.1515/gmj.2003.257.
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Abstract Basic static boundary value problems of elasticity are considered for a semi-infinite curvilinear prism Ω = {ρ 0 < ρ < ρ 1, α 0 < α < α 1, 0 < 𝑧 < ∞} in generalized cylindrical coordinates ρ, α, 𝑧 with Lamé coefficients ℎ ρ = ℎ α = ℎ(ρ, α), ℎ𝑧 = 1. It is proved that the solution of some boundary value problems of elasticity can be reduced to the sum of solutions of other boundary value problems of elasticity. Besides its cognitive significance, this fact also enables one to solve some non-classical elasticity problems.
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XIA, BINGXING, and VIET HA HOANG. "BEST N-TERM GPC APPROXIMATIONS FOR A CLASS OF STOCHASTIC LINEAR ELASTICITY EQUATIONS." Mathematical Models and Methods in Applied Sciences 24, no. 03 (December 29, 2013): 513–52. http://dx.doi.org/10.1142/s0218202513500589.
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We consider a class of stochastic linear elasticity problems whose elastic moduli depend linearly on a countable set of random variables. The stochastic equation is studied via a deterministic parametric problem on an infinite-dimensional parameter space. We first study the best N-term approximation of the generalized polynomial chaos (gpc) expansion of the solution to the displacement formula by considering a Galerkin projection onto the space obtained by truncating the gpc expansion. We provide sufficient conditions on the coefficients of the elastic moduli's expansion so that a rate of convergence for this approximation holds. We then consider two classes of stochastic and parametric mixed elasticity problems. The first one is the Hellinger–Reissner formula for approximating directly the gpc expansion of the stress. For isotropic problems, the multiplying constant of the best N-term convergence rate for the displacement formula grows with the ratio of the Lamé constants. We thus consider stochastic and parametric mixed problems for nearly incompressible isotropic materials whose best N-term approximation rate is uniform with respect to the ratio of the Lamé constants.
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Peherstorfer, F. "Explicit generalized zolotarev polynomials with complex coefficients." Constructive Approximation 13, no. 2 (June 1997): 261–69. http://dx.doi.org/10.1007/bf02678468.
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Peherstorfer, F. "Explicit Generalized Zolotarev Polynomials with Complex Coefficients." Constructive Approximation 13, no. 2 (July 1, 1997): 261–69. http://dx.doi.org/10.1007/s003659900042.
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Ramachandran, C., T. Soupramanien, and J. Sokół. "On a Generalization of Bounded Univalent Function of Complex Order." Journal of Computational and Theoretical Nanoscience 15, no. 2 (February 1, 2018): 601–5. http://dx.doi.org/10.1166/jctn.2018.7130.
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In this paper, we introduce a new class of analytic functions of complex order involving a family of generalized differential operators and we discuss the sufficient conditions, estimation of coefficients. The motivation of this paper is to generalize the Coefficient Estimates obtained by Attiya, and Aouf et al. by making use of the generalized differential operator Dnλ, μ.
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Deniz, Erhan, Jay M. Jahangiri, Samaneh G. Hamidi, and Sibel K. Kına. "Faber polynomial coefficients for generalized bi-subordinate functions of complex order." Journal of Mathematical Inequalities, no. 3 (2018): 645–53. http://dx.doi.org/10.7153/jmi-2018-12-49.
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Zhang, Sheng, Lijie Zhang, and Bo Xu. "Rational Waves and Complex Dynamics: Analytical Insights into a Generalized Nonlinear Schrödinger Equation with Distributed Coefficients." Complexity 2019 (March 21, 2019): 1–17. http://dx.doi.org/10.1155/2019/3206503.
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In this paper, we first present a complex multirational exp-function ansatz for constructing explicit solitary wave solutions, N-wave solutions, and rouge wave solutions of nonlinear partial differential equations (PDEs) with complex coefficients. To illustrate the effectiveness of the complex multirational exp-function ansatz, we then consider a generalized nonlinear Schrödinger (gNLS) equation with distributed coefficients. As a result, some explicit rational exp-function solutions are obtained, including solitary wave solutions, N-wave solutions, and rouge wave solutions. Finally, we simulate some spatial structures and dynamical evolutions of the modules of the obtained solutions for more insights into these complex rational waves. It is shown that the complex multirational exp-function ansatz can be used for explicit solitary wave solutions, N-wave solutions, and rouge wave solutions of some other nonlinear PDEs with complex coefficients.
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Polosin, V. G. "Shape measures of generalized beta distributions." Journal of Physics: Conference Series 2094, no. 2 (November 1, 2021): 022009. http://dx.doi.org/10.1088/1742-6596/2094/2/022009.
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Abstract This paper presents shape measures for generalized beta distributions that unit many subfamilies of distributions. For the study of complex systems, the information entropy of the whole family of the generalized beta distribution is obtained. The paper uses the interval of entropy uncertainty as an estimate of the entropy uncertainty for probable models, which are given in units of an observable random variable. The entropy uncertainty interval was used to construct the entropy coefficient of unbiased subfamilies of the generalized beta distribution. Particular entropy coefficients are given for frequently used subfamilies of beta distribution, that greatly facilitates the use of coefficients as independent information measures in determining the shape of models. The paper contains the most general formulas for probabilistic measures of the distributions shape also.
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Teshaev, Muhsin, Ismoil Safarov, Dilshoda Ibragimova, Doniyor Rayimov, and Sharif Akhmedov. "Stationary response of the system “Cylindrical shell – viscoelastic filler” to the effect of a moving load." Journal of Physics: Conference Series 2697, no. 1 (February 1, 2024): 012004. http://dx.doi.org/10.1088/1742-6596/2697/1/012004.
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Abstract The paper considers the stationary response of the system “cylindrical shell - viscoelastic filler” to the action of a moving load. The filler and the shell were assumed to be viscoelastic. Using the principle of analogy of viscoelastic and elastic problems (elastic-viscoelastic analogy), a stationary solution of the action of mobile loads on a shell with a viscoelastic filler is obtained. It is shown that this principle makes it possible to generalize the class of problems obtained for the case of viscoelastic media. Since the viscoelastic filler has damping properties, the inversion integrals have no singularities on the real axis, and the elements of the determinants in integrals become complex since in this problem in the image space, the Lame coefficients are complex and depend on the speed of the load movement, as well as the Fourier transform parameter. Numerical results are obtained, and an analysis is made.
Dissertations / Theses on the topic "Generalized complex Lamé coefficients"
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Bouzzit, Aziz. "Ellipsométrie acoustique pour le suivi et la caractérisation de matériaux complexes." Electronic Thesis or Diss., CY Cergy Paris Université, 2024. http://www.theses.fr/2024CYUN1304.
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Les matériaux complexes sont aujourd'hui au cœur des enjeux sociétaux majeurs dans la plupart des grands domaines tels que l'énergie, le transport, l'environnement, la conservation/restauration du patrimoine, la santé ou la sécurité. En effet, de par les opportunités d'innovation offertes en matière de fonctionnalités, ces matériaux suscitent de nouvelles problématiques d'analyse et de compréhension multi-physiques et multi-échelles. Il en va de même pour l'instrumentation nécessaire à leur caractérisation.Répandues dans le domaine de la caractérisation non destructive des milieux complexes, les méthodes acoustiques utilisent les propriétés de propagation des ondes mécaniques dans ces matériaux pouvant être hétérogènes et anisotropes.Dans une approche multi-échelle, l'intérêt des méthodes ultrasonores est d'être particulièrement sensibles à leurs propriétés mécaniques, telles que l'élasticité, la rigidité et la viscosité. La nature hétérogène et multiphasique d'un milieu complexe conduit ainsi à la notion de milieu viscoélastique, caractérisé par les coefficients de Lamé généralisés complexes (��∗, ��∗) et leur variation en fonction de la fréquence.L'objectif de cette thèse est de développer une méthode de caractérisation de ces matériaux complexes viscoélastiques qui permette de mesurer simultanément la variation des deux coefficients de Lamé généralisés complexes (��∗, ��∗) en fonction de la fréquence. L'approche proposée est de suivre, dans l'espace et dans le temps, la propagation de l'onde de Rayleigh et d'extraire ses paramètres ellipsométriques (ellipticité χ et orientation θ) en complément des paramètres propagatifs (k' et k'') classiquement déterminés. Basée sur la détection de l'onde par vibrométrie laser 3D à la surface du matériau complexe, et au moyen de l'analyse de Gabor 2D dans l'espace des Quaternions, l'estimation de l'ensemble des paramètres - propagatifs et ellipsométriques - donne accès à la caractérisation complète du milieu avec cette seule onde de Rayleigh.Les développements théoriques proposés dans ce travail, ainsi que les résultats expérimentaux et issus de simulation, confirment l'intérêt de l'ellipsométrie acoustique pour la caractérisation de ces matériaux complexesComplex materials are at the heart of major societal challenges in most major fields such as energy, transport, environment, heritage conservation/restoration, health and safety. Because of the opportunities for innovation offered in terms of features, these materials are giving rise to new problems of multi-physical and multi-scale analysis and understanding. The same applies to the instrumentation needed to characterize them.Acoustic methods, which are widely used in the non-destructive characterization of complex media, make use of the propagation properties of mechanical waves in these materials, which can be heterogeneous and anisotropic.In a multi-scale approach, the advantage of ultrasonic methods is that they are particularly sensitive to mechanical properties such as elasticity, rigidity and viscosity. The heterogeneous and multiphase nature of a complex medium thus leads to the notion of a viscoelastic medium, characterized by generalized complex Lamé coefficients (��∗, ��∗) and their variation as a function of frequency.The objective of this thesis is to develop a method for characterizing these complex viscoelastic materials that simultaneously measures the variation of the two generalized complex Lamé coefficients (��∗, ��∗) versus the frequency. The proposed approach is to follow, in space and in time, the propagation of the Rayleigh wave and to extract its ellipsometric parameters (ellipticity χ and orientation θ) in addition to the propagation parameters (k' and k'') conventionally determined. Based on the wave detection by 3D laser vibrometry at the surface of the complex material, and by means of 2D Gabor analysis in Quaternion space, the estimation of propagation and ellipsometric parameters gives access to the complete characterization of the complex material only by studying the interaction of a Rayleigh wave with the medium.The theoretical developments proposed in this work, together with experimental and simulation results, confirm the value of acoustic ellipsometry for characterizing these complex materials
Books on the topic "Generalized complex Lamé coefficients"
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Wüstholz, Gisbert, and Clemens Fuchs, eds. Arithmetic and Geometry. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691193779.001.0001.
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This book presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures—which were delivered in celebration of the tenth anniversary of the annual summer workshops in Alpbach, Austria—provide an introduction to high-level research on three topics: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings heights and L-functions. The book consists of notes, written by young researchers, on three sets of lectures or minicourses given at Alpbach. The first course contains recent results dealing with the local Langlands conjecture. The fundamental question is whether for a given datum there exists a so-called local Shimura variety. In some cases, they exist in the category of rigid analytic spaces; in others, one has to use Scholze's perfectoid spaces. The second course addresses the famous Pell equation—not in the classical setting but rather with the so-called polynomial Pell equation, where the integers are replaced by polynomials in one variable with complex coefficients, which leads to the study of hyperelliptic continued fractions and generalized Jacobians. The third course originates in the Chowla–Selberg formula and relates values of the L-function for elliptic curves with the height of Heegner points on the curves. It proves the Gross–Zagier formula on Shimura curves and verifies the Colmez conjecture on average.
Book chapters on the topic "Generalized complex Lamé coefficients"
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Ignatidis, Panagiotis, Henrik von der Haar, Christoph Hennecke, and Friedrich Dinkelacker. "Impact of Mixing on the Signature of Combustor Defects." In Regeneration of Complex Capital Goods, 95–113. Cham: Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-51395-4_6.
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AbstractDefects in the combustion chamber can negatively influence the performance of an aircraft engine and increase component stress in the turbine. One aim of the Collaborative Research Center 871 is to provide early prediction about the condition of the engine by analysing the signature of the exhaust gas jet. This includes the usage of machine learning techniques and helps to optimise maintenance times and to reduce costs. This topic is linked to the question, how defects in the combustion chamber affect the flow field and how the defect signature is mixed out in the hot gas path. Examples are shown for a simplified ring burning chamber, where several experimental and numerical studies have been done. Additionally, one failure case is described in detail here, where the methodology is applied to a real size gas turbine burning chamber and its subsequent turbine. Furthermore the diffusion theory is generalized to situations with complex geometrical boundary conditions, for instance from the turbine passage channel geometry. This approach is applied on the investigated example case and shows complex thermal diffusion coefficients, being in the order of 10,000–100,000 times larger than the molecular diffusion coefficient. Even these large values allow the determination of burning chamber defects from the exhaust flow pattern.
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Egelstaff, P. A. "Collective modes of motion at low frequencies." In An Introduction To The Liquid state, 280–95. Oxford University PressOxford, 1992. http://dx.doi.org/10.1093/oso/9780198510123.003.0014.
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Abstract The thermal motion in a liquid may be divided conveniently into singleparticle and collective modes of motion, and the next two chapters will be devoted to a discussion of the latter modes. This subject is a complex one, and there is an extensive literature (e.g. Boon and Yip 1980). The treatment given here is subdivided into the macroscopic modes, which may be described by hydrodynamic theory, and the microscopic modes, for which the theory is less exact. A part of this discussion concerns the processes—viscosity and thermal conduction—by which these modes are damped. The viscosity coefficient will be discussed at length, but because the theory of the thermal conductivity is more complex, it will be treated superficially. For the hydrodynamic theory these coefficients are taken as given constants from which the magnitude of the mode damping coefficients may be calculated. In this chapter microscopic definitions of these transport coefficients will be given and later generalized for discussion of the microscopic modes of motion.
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Kwitt, Roland, Peter Meerwald, and Andreas Uhl. "Blind Detection of Additive Spread-Spectrum Watermarking in the Dual-Tree Complex Wavelet Transform Domain." In Crime Prevention Technologies and Applications for Advancing Criminal Investigation, 53–65. IGI Global, 2012. http://dx.doi.org/10.4018/978-1-4666-1758-2.ch005.
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In this paper, the authors adapt two blind detector structures for additive spread-spectrum image watermarking to the host signal characteristics of the Dual-Tree Complex Wavelet Transform (DT-CWT) domain coefficients. The research is motivated by the superior perceptual characteristics of the DT-CWT and its active use in watermarking. To improve the numerous existing watermarking schemes in which the host signal is modeled by a Gaussian distribution, the authors show that the Generalized Gaussian nature of Dual-Tree detail subband statistics can be exploited for better detector performance. This paper finds that the Rao detector is more practical than the likelihood-ratio test for their detection problem. The authors experimentally investigate the robustness of the proposed detectors under JPEG and JPEG2000 attacks and assess the perceptual quality of the watermarked images. The results demonstrate that their alterations allow significantly better blind watermark detection performance in the DT-CWT domain than the widely used linear-correlation detector. As only the detection side has to be modified, the proposed methods can be easily adopted in existing DT-CWT watermarking schemes.
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Zinn-Justin, Jean. "Large order behaviour of perturbation theory." In Quantum Field Theory and Critical Phenomena, 960–74. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198834625.003.0040.
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In quantum field theory (QFT), the main analytic tool to calculate physical quantities is the perturbative expansion. Following, Dyson's intuitive argument, the divergence of perturbative series was demonstrated in some models of quantum mechanics (QM) with polynomial potentials, using the Schrödinger equation. Later, it was proposed to study the problem within a path integral formulation. A systematic method in field theory was proposed by Lipatov, using the field integral representation of the φ4 4 field theory and instantons. It can be shown that the ground-state energy of the quartic anharmonic oscillator is analytic in a cut-plane. The imaginary part of the energy on the cut is related to barrier penetration. The behaviour of the perturbative coefficients at large orders is related to the behaviour of the imaginary part for small and negative coupling and can be obtained by instanton methods. The method has been generalized to the class of potentials for which (in general complex) instanton contributions have been calculated. The same method can be readily applied to boson field theories, while the extension to field theories involving fermions, like Quantum QED, requires additional considerations. The general conclusion is that, in QFT, all perturbative series, expanded in terms of a loop-expansion parameter, are divergent series.
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Criss, Robert E. "Nonequilibrium Fractionation and Isotopic Transport." In Principles of Stable Isotope Distribution. Oxford University Press, 1999. http://dx.doi.org/10.1093/oso/9780195117752.003.0006.
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At the Earth’s surface, isotopic disequilibrium is far more common than isotopic equilibrium. Although isotopic equilibrium is approached in certain instances, numerous constituents of the lithosphere, hydrosphere, atmosphere, and biosphere are simply not in mutual isotopic equilibrium. This condition is consistent with the complex and dynamic conditions typical of the Earth’s surface, particularly the large material fluxes, the rapid changes in temperature, and the biological mediation of chemical systems. Fortunately, several aspects of isotopic disequilibrium may be understood in terms of elementary physical laws. For homogeneous phases such as gases or well-stirred liquids, or for cases where spatial gradients in isotopic contents are not of primary interest, then the principles of elementary kinetics can be applied. For cases where isotopic gradients are important, the laws of diffusion are applicable. If two phases are out of isotopic equilibrium, they will progressively tend to approach the equilibrium state with the passage of time. This phenomenon occurs by the process of isotopic exchange, and its rate may be understood by examining isotopic exchange reactions from the viewpoint of elementary kinetic theory. In particular, consider the generalized exchange reaction where A and B are two phases that share a common major element, and A* and B* represent the same phases in which the trace isotope of that element is present. The present analysis is simplified if the exchange reaction is written so that only one atom is exchanged, in which case the stoichiometric coefficients are all unity. For reaction 4.1, kinetic principles assert that the forward and reverse reactions do not, in general, proceed at identical rates, but rather at the rates indicated by the quantities kα and k written by the arrows, multiplied by the appropriate concentrations terms. Assuming that the reaction is first order, then the reaction progress, represented by the quantity dA*/dt, may be expressed by the difference between these forward and reverse rates, as follows: . . . dA*/dt = kα(A)(B*) − k(A*)(B) (4.2) . . . In order to evaluate the exchange process more completely, is important to carefully chose a consistent set of concentrations for substitution equation 4.2.
Conference papers on the topic "Generalized complex Lamé coefficients"
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Hiremath, Nandeesh, Nicholas Motahari, and Narayanan Komerath. "Generalized Approach for Slung-Load Aerodynamics." In Vertical Flight Society 72nd Annual Forum & Technology Display, 1–12. The Vertical Flight Society, 2016. http://dx.doi.org/10.4050/f-0072-2016-11563.
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The general problem of measuring bluff-body aerodynamic load maps is considered, and simplified using a Fourier series representation Six-component aerodynamic load coefficients have been measured in a low-speed wind tunnel with 1 degree azimuthal resolution, about the needed axes for over 30 models using the Continuous Rotation method. Test cases include both explorations on practical vehicle shapes, and systematic parameter variations on canonical shapes, including open and closed cylinders, flat and long rectangular containers. From the load maps for different aspect ratios, different approaches to interpolation and generalization are considered. Interpolating Fourier coefficients proves to be efficient and accurate. The efficacy of such interpolation is shown where the aerodynamics on an empty engine canister are quickly estimated by reference to the interpolated data for a circular cylinder of aspect ratio 1.9. The possibility of using combinations of canonical shapes to approximate the load map for a complex object such as a road vehicle, is also seen from the success of a combination of airloads for a cylinder and rectangular box, in approximating several of the aerodynamic load coefficient variations for a road vehicle model.
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Su, Shigong, and Xianzhong Su. "Generalized Characteristic Method for Orthotropic Media." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0549.
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Abstract A new method is developed to solve two dimensional transient problems of elastodynamics in orthotropic media. The real solutions of the characteristic equation for the Navier equations in orthotropic media can be analytically continued to the complex domain in which they are called generalized characteristics. The generalized characteristics are employed to prove that a set of algebraic equations of the velocity components is equivalent to the Navier equations. To illustrate how to use the present method in elastodynamics for orthotropic media, the problems of time domain Green’s functions in an unbounded medium, and Lamb’s problem for a buried concentrated line force are solved by applying the derived algebraic equations. The reflection coefficients and Snell’s law on the surface of a half-space are obtained for incident non-plane transient waves. The direct waves, reflected waves, and head wave in a half-space are analyzed directly in terms of generalized characteristics. Finally, some numerical results for the particle displacement at receivers (on and below the surface) are shown for four typical crystals and composite materials.
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Blumenthal, Robert F., Michal Siorek, and Sunil Patil. "Framework for Machine Learning-Based Turbulence Modeling to Accurately Predict the Complex Flows in Gas Turbines." In ASME Turbo Expo 2024: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/gt2024-128443.
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Abstract Flow in turbomachinery such as industrial gas turbines is highly complex and exhibits different characteristics for different operating conditions within a duty cycle or performance range. This poses a challenge to predict the performance of the machine accurately and efficiently. Computational Fluid Dynamics (CFD) has been successfully used for aerothermal analysis of turbomachinery successfully. An important aspect of CFD analysis is setting best practice for turbulence models for a given range of the machine especially in a RANS (Reynolds Averaged Navier-Stokes) framework. This is usually a manual process and can be very time consuming based on the complexity of the flow. The ability in many of these turbulence models to adapt the model coefficients to a specific application, such as a gas turbine, is limited. A novel approach is presented in this paper that uses a unique turbulence modeling paradigm and machine learning to accurately and efficiently predict complex flows over a wide range. The new Generalized k-ω (GEKO) turbulence model is unique in that it exposes key and selective coefficients that control the behavior of different flows that may be encountered in gas turbines, such as free shear flow and near-wall flow. This paper provides a generic framework to optimize these key coefficients via neural network-based machine learning algorithm while leveraging available experimental or benchmark data. This approach is applied to an industrial gas turbine exhaust diffuser. Comparisons of the flow predictions using this approach are done against the experimental data for design/off-design conditions.
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Sutulo, Serge, and C. Guedes Soares. "A Generalized Strip Theory for Curvilinear Motion in Waves." In ASME 2008 27th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/omae2008-57936.
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A simulation-oriented mathematical model for a slender ship manoeuvring in waves was devised as a fusion of two classic linear strip theory implementations used separately in manoeuvring and seakeeping. Two basic requirements were formulated: the generalized model must reduce to the popular Salvesen–Tuck–Faltinsen seakeeping model in the particular case of the rectilinear base motion (constant speed advance) and to the Munk theory in absence of waves and wave-induced motions. It was assumed that the generalized model will then be reasonably consistent in intermediate regimes. The primary problem formulation was performed under the assumption that small-amplitude oscillations with the encounter frequency in regular seas are superimposed with the arbitrary base manoeuvring motion characterized by slowly-varying kinematic parameters. After the velocity potential’s decomposition into the quasi-steady and substantially unsteady parts, application of the Bernoulli equation, and further integration over the wetted surface (which can be taken in its equilibrium or instantaneous position) result in the representation of hydrodynamic forces in the frequency domain through longitudinal distributions of the sectional complex added masses and their longitudinal derivatives. The frequency-dependent coefficients are then approximated with rational fractions and, further, subjected to the Fourier transform. As a result, a set of ordinary differential equations for the time-dependent hydrodynamic forces and auxiliary state variables were obtained. The model was implemented as part of a manoeuvring simulation code and some time histories of various components of the hydrodynamic forces are given as illustrations.
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Gamo, Hideya. "Quasi-evanescent waves of the total internal reflection at the lossy or gain medium." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1986. http://dx.doi.org/10.1364/oam.1986.fx3.
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The propagation constant β = ω μ 0 ε in the lossy or gain medium is a complex quantity, of which the imaginary part represents damping or growing amplitude. The propagation constant in the free space β 0 = ω μ 0 ε 0 is real, but the component of propagation constant parallel to the boundary surface is a complex quantity, because of the continuity of tangential components of the propagation vectors: β1 t = β2 t (generalized Snell’s law). Consequently, the normal component of propagation vector β 2 n = ( β 0 2 − β 2 t 2 ) 1 / 2 becomes complex. By using the wave impedances ηTM= β n /ωϵand ηTE= ω μ /β n for TM and TE waves, we obtain the complex reflection and transmission coefficients (generalized Fresnel formulas). In the case of total internal reflection at lossless media, β2 t is real and greater than β0, and hence β2 n is imaginary. This is the well-known evanescent damping. In the case of lossy or gain medium, however, β2 n becomes a complex quantity. The waves outside lossy or gain media are not perfectly evanescent but contain some radiating components. This phenomena which corresponds to the leaky surface waves will be compared with observation using an absorbing 90° prism.
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Zvorykin, Alexander, Roman Popov, Mykola Bobyr, and Igor Pioro. "Low-Cycle Strength of Elements of Constructions." In 2018 26th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/icone26-81860.
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Analysis of engineering approach to the operational life forecasting for constructional elements with respect to the low-cycle fatigue is carried out. Applicability limits for a hypothesis on existence of generalized cyclic-deforming diagram in case of complex low-cycle loading (deforming) are shown. It is determined, that under condition of plane-stress state and piecewise-broken trajectories of cycle loading with stresses and deformation checking the cyclic deforming diagram is united in limits of deformations, which are not exceeded 10 values of deformation corresponding material yield point. Generalized kinematic equation of material damageability is described. The method of damageability parameter utilization for increasing of accuracy calculation of structural elements low-cycle fatigue by using the effective coefficients of stresses and deformations taking into account the damageability parameter is given.
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Dávid, Alexandra, and S. C. Sinha. "Some Ideas on the Local Control of Nonlinear Systems With Time-Periodic Coefficients." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8381.
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Abstract In this paper ideas on local control of linear and nonlinear time-periodic systems are presented. Our first goal is to stabilize the system far away from bifurcation points. In this case, the classical linear state feedback stabilization based on pole placement is generalized such that it is applicable to time-periodic systems. The linear state-feedback controller design involves computation of the fundamental solution matrix of the system in a symbolic form as function of the control parameters. Next, we focus on the bifurcation control of time-periodic systems. When the linearized system is in a critical case of stability (i.e. when it has Floquet multipliers on the unit circle of the complex plane) and the critical modes are uncontrollable in the linear sense, then a purely nonlinear state-feedback controller is designed to stabilize the equilibrium at the bifurcation point and ensure the stability of the bifurcated nontrivial solution. When the linearized system is linearly controllable, then it is shown that an appropriately chosen linear state-feedback control can also modify the nonlinear features of the bifurcations, such as stability or size of the limit cycles or quasi-periodic limit sets. The control techniques are based on a series of transformations that convert the system into a time-invariant form. First, the Lyapunov-Floquet transformation is used to make the linear part of the periodic system time-invariant. Then, time-periodic center manifold reduction and time-dependent normal form theory are applied to obtain the simplest nonlinear form of a system undergoing bifurcation. For most codimension one bifurcations the normal form is completely time-invariant and therefore, it is a rather simple task to choose the appropriate control gains. These ideas are illustrated by an example of a parametrically excited simple pendulum undergoing symmetry breaking bifurcation.
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Panza, Michael J. "Eigenstructure Calculation for Mixed Vibratory Systems Composed of a Continuous Beam and Concentrated Actuators." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21570.
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Abstract A calculation of the eigenstructure for mixed vibratory systems composed of a continuous beam and concentrated actuators is presented. The combined distributed and lumped element systems include actuators for active vibration control. The focus of this paper is on open loop models where with zero voltage input to the actuators. The continuous beam is isolated and discretized via modal analysis and combined with the actuator dynamics to form an asymmetric system. The resulting system is cast into a generalized nondimensional form suitable for studying system behavior for a broad range of system parameters. The solution is expressed as a series using the isolated beam mode eigenfunctions as a basis. The coefficients in the series are obtained from the complex eigensolution of the asymmetric system. Two examples are used to show a comparison of the complex mixed system and real isolated beam natural frequencies and mode shapes. The effect of beam and actuator parameter values are investigated via a key dimensionless parameter.
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Yosibash, Zohar, and Barna A. Szabó. "Failure Analysis of Composite Materials and Multi Material Interfaces." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0145.
Full textAbstract:
Abstract Composite materials and multi-material interface problem usually have one or more singular points. In the neighborhood of these points the solution of two-dimensional linear elastostatic problems is characterized by a series of eigenpairs and their coefficients, called the generalized stress intensity factors (GSIFs). Accurate and reliable computation of the eigenpairs and the GSIFs is important because failure theories directly or indirectly involve these quantities. New efficient and accurate methods for numerical computation of the eigenpairs and the GSIFs, based on the p-version of the finite element method, are presented and demonstrated. Examples, representing two different kinds of singular points demonstrate that the method works well and produces results of high accuracy. Importantly, the method is applicable to anisotropic materials, multi-material interfaces, and cases where the singularities are characterized by complex eigenpairs.
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Belloli, Alberto, Oliver Thomaschewski, and Paolo Ermanni. "Optimum Placement of Piezoelectric Ceramic Modules for Vibration Suppression of Highly Constrained Structures." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84614.
Full textAbstract:
The vibration suppression efficiency of so-called shunted piezoelectric systems is decisively influenced by the number, shape, dimension, and position of the implemented piezoelectric ceramic elements. This paper presents a procedure based on evolutionary algorithms for optimum placement of piezoelectric ceramic modules on real-world, highly constrained lightweight structures. The optimization loop includes the CAD software CATIA V5, the FE package ANSYS and DynOPS, a proprietary software tool able to connect the Evolving Object library with any simulation software that can be started in batch-mode. A user-defined piezoelectric shell element is integrated into ANSYS 8.1. Modal generalized electromechanical coupling coefficients are used as optimization objective and constraints. Position, dimension and shape of commercial, customized and free-form patches are determined for optimum multi-mode vibration suppression of a pinned, quadratic plate. An aircraft fuselage panel with a window cutout is investigated as test object for complex, curved geometries.