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It has been known that the axisymmetric Cauchy–Poisson problem for dispersive water waves is well posed in the sense of stability. Thereby time evolution solutions of wave propagation depend continuously on initial conditions. However, in this paper, it is demonstrated that the axisymmetric Cauchy–Poisson problem is ill posed in the sense of stability for a certain class of initial conditions, so that the propagating solutions do not depend continuously on the initial conditions. In order to overcome the difficulty of the discontinuity, Landweber–Fridman's regularization, famous and well known in applied mathematics, are introduced and investigated to learn whether it is applicable to the present axisymmetric wave propagation problem. From the numerical experiments, it is shown that stable and accurate solutions are realized by the regularization, so that it can be applicable to the determination of the ill-posed Cauchy–Poisson problem. 相似文献
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To assist in the prototyping and controller design of point-absorber wave energy converters (WECs), an easy-to-implement hybrid integral-equation method is presented for computing the frequency-domain hydrodynamic properties of bodies with a vertical axis of symmetry in waves. The current hybrid method decomposes the flow domain into two parts: an inner domain containing the body and an outer domain extending to infinity. The solution in the inner domain is computed using the boundary-element method, and the outer-domain solution is expressed using eigenfunctions. Proper matching at the domain boundary is achieved by enforcing continuity of velocity potential and its normal derivative. Body symmetry allows efficient computation using ring sources in the inner domain. The current method is successfully applied to three different body geometries including a vertical truncated floating cylinder, the McIver toroid, and the coaxial-cylinder WEC being developed in the authors’ laboratory. In particular, the current results indicate that, by replacing the flat bottom of the coaxial-cylinder WEC with the Berkeley-Wedge (BW) shape, viscous effect can be significantly reduced with only minor negative impact on wave-exciting force, thus increasing WEC efficiency. Finally, by comparing to experimental measurements, the current method is demonstrated to accurately predict the heave added mass and wave-exciting force on the coaxial-cylinder WEC with BW geometry. If a viscous damping correction factor is used, the heave motion amplitude can also be accurately computed. 相似文献
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An important question regarding the study of mean field dynamo models is how to make precise the nature of their underlying dynamics. This is difficult both because relatively little is known about the dynamical behaviour of infinite dimensional systems and also due to the numerical cost of studying the related partial differential equations.
As a first step towards their understanding, it is useful to consider the corresponding truncated models. Here we summarise some recent results of the study of a class of truncated axisymmetric mean field dynamo models. We find conclusive evidence in these models for various types of intermittency as well as multiple attractors and final state sensitivity.
We also find that the understanding of the underlying dynamics of such dynamo models requires the study of a new class of dynamical systems, referred to as the non-normal systems. Current work demonstrates that these types of systems are capable of a novel type of intermittency and also of relevance for the understanding of the full axisymmetric PDE dynamo models. 相似文献
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The challenges for determining the mechanical behavior of flexible pipes mainly arise from highly non-linear geometrical and material properties and complex contact interaction conditions between and within layers components. This paper develops an innovative model to investigate the linear viscoelastic behavior of flexible pipes under axisymmetric loads in time domain. The model is derived from an equivalent linear elastic axisymmetric model by invoking the elastic-viscoelastic correspondence principle. Analytical formulations that describe the behavior of the metallic helical layers based on a combination of differential geometry concepts and Clebsch–Kirchhoff equilibrium equations for initially curved slender elastic rods are presented. The elastic response of the homogenous polymeric cylindrical layers is also presented. The assemblage of both types of governing algebraic equations that approximate analytical solutions for force and moment distributions, deformations in each layer, as well as contact pressure between near layers, taking time-dependent characteristics of polymeric layers into account are provided and it is clear that the relationship between axial force and elongation is non-linear and encompasses a hysteretic response. Besides, the creep behavior in axial direction can also be found. Some insights into the differences in the behavior for several loading conditions are discussed by considering variable frequencies. 相似文献
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A method is presented of estimating the responses of axisymmetric bodies floating in spread irregular seas, using a Laplace transfer-function formulation of a floating body time-domain model. A general-case spread-wave model is formulated, using separate wave excitation transfer functions, and a simplification of this approach is proposed, reducing both model complexity and computation time. Responses are computed using both approaches and a comparison made to assess the circumstances in which the simplified approach may be used effectively. The results are also interpreted to highlight the implications of using an equivalent unidirectional wave as an approximation to a spread wave. 相似文献
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By using the axisymmetric finite elements static limit analysis formulation, proposed recently by the authors, the stability numbers (γH/co) for an unsupported vertical circular excavation in clays, whose cohesion increases with depth, have been determined under undrained condition; γ = unit weight, H = height of the excavation and co = cohesion along ground surface. The results are obtained for various values of H/b and m; where b = the radius of the excavation and m = a non-dimensional parameter which accounts for the rate of the increase of cohesion with depth. The values of the stability numbers increase continuously both with increases in H/b and m. The results obtained in this study compare well with those available in literature. 相似文献
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R. Shafaghat S.M. HosseinalipourI. Lashgari A. Vahedgermi 《Applied Ocean Research》2011,33(3):193-198
The reduction of energy consumption for high speed submersible bodies is an important challenge in hydrodynamic researches. Supercavitation is a hydrodynamic process in which a submerged body gets enveloped in a layer of gas. As the density and viscosity of the gas is much lower than that of seawater, skin friction drag can be reduced considerably. If the nose of the body (cavitator) has a proper shape, the attendant pressure drag remains at a very low value, so the overall body drag reduces significantly. Total drag force acting on the supercavitating self-propelled projectiles dictates the amount of fuel consumption and thrust requirements for the propulsion system to maintain a required cavity at the operating speed. Therefore, any reduction in the drag coefficient, by modifying the shape of the cavitator to achieve optimal shape, will lead to a decrease of this force. The main objective of this study is to optimize the axisymmetric cavitator shape in order to decrease the drag coefficient of a specified after-body length and body velocity in the axisymmetric supercavitating potential flow. To achieve this goal, a multi-objective optimization problem is defined. NSGA II, which stands for Non-dominated Sorting Genetic Algorithm, is used as the optimization method in this study. Design parameters and constraints are obtained according to the supercavitating flow characteristics and cavitator modeling. Then objective functions will be generated using the Linear Regression Method. The results of the NSGA II algorithm are compared with those generated by the weighted sum method as a classic optimization method. The predictions of the NSGA II algorithm seem to be excellent. As a result, the optimal cavitator’s shapes are similar to a cone. 相似文献
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The galactic dynamical system expressed by a third-order axisymmetric polynomial potential is investigated numerically by computing periodic solutions. We define as Sthe compact set of initial conditions generating bounded motions, and as S p , with S p ? S, the countable set of all initial conditions generating periodic solutions. Then, we consider the subsets S s p and S a p of S p , where S s p ∪ S a p = S p , S s p S a p = Ø, the first of which corresponds to symmetric periodic solutions, and the second to asymmetric solutions. Then, we approximate the set S s p , leaving treatment of the set S a p of asymmetric solutions for a future publication. The set S s p is known to be dense in S (‘Last Geometric Theorem of Poincar;’, Birkhoff, 1913). Using a computer programme capable to locate all elements of the set S s p that generate symmetric periodic solutions that re-enter after intersecting the axis of symmetry from 1 to ntimes. The results of the approximation of S s p in the total domain and in the sample sub-domains of zooming, we present in graphical form as family curves in the (x, C) plane. The solutions located with the largest periods re-enter after 440 galaxy revolutions while the families calculated fully (initial conditions, period, energy, stability co-efficient) include solutions that re-enter after 340 galaxy revolutions. To advance further the approximation of the set S s p thus obtained, we applied the same procedure inside eight sub-domains of the domain Sinto which we ‘zoomed’ through selection of finer search steps and double maximum periods. The family curves thus calculated presented in the (x, C) plane do not intersect anywhere in some sub-domains and their pattern resembles that of laminar flow. In other sub-domains, however, we found family curves from which branching families emanate. The concepts of completeand non-completeapproximation of S s p in sub-domains of laminar and sub-domains with branching family curves, respectively, is introduced. Also, the concept of basic family of order1, 2, ..., n, are defined. The morphology of individual periodic solutions of all families is investigated, and the types of envelopes found are described. The approximate set S s p was also checked by computing Poincar; sections for energy values corresponding to the mean energy range of the eight sub-domains of zooming mentioned above. These sections show that most parts of the compact domain in Sgenerating non-periodic but bounded solutions correspond to with well-shaped tori that intersect the x-axis, a fact that implies that dominant to exclusive type of periodic solutions are the symmetric ones with two normal crossings of this axis. The presence of non-symmetric periodic solutions as well as of chaotic regions is encountered. All calculations reported here were performed using the variable step R-K 8th-order direct integration and setting the allowable energy variation Δ C= |C start? C end| < 10?13. The output, consisting of many thousands of families and their properties (initial conditions, morphology, stability, etc.), is stored in a directory entitled ‘Atlas of the Symmetric Periodic Solution of the Galactic Motion Problem’. 相似文献