In an electron storage ring, the emittances are determined by the beam energy and the linear lattice; the effects of lattice nonlinearity are usually negligible. In this study, we show a case where ...the vertical emittance has a strong quadratic dependence on the vertical chromaticity, a form of lattice nonlinearity. In this case, a crab cavity is present in the lattice, which couples the longitudinal and vertical motions of the beam. A theoretic analysis is conducted to derive the emittance dependence on chromaticity, using the normal form approach to decouple the longitudinal and vertical motion. Particle tracking simulations are performed to verify the analytic results and a good agreement is found. The dependence of equilibrium emittances on nonlinear lattice properties as demonstrated in this paper may provide new possibilities for design options and machine control.
For a boundary value problem of nonlinear composite beam, the boundary conditions are fulfilled automatically by a boundary shape function (BSF), which includes exact solution as a member. For any ...given free function, we develop a method to construct the BSF and derive two iterative algorithms to approximate the exact solution. Let the solution be a BSF and then the free function be a new variable. Consequently, we can exactly convert the nonlinear-nonuniform composite beam equation, subjecting to nonlinear boundary conditions, to a corresponding initial value problem for the new variable with its terminal values deemed as unknown parameters in the ordinary differential equations (ODEs), whereas the initial conditions are given. In doing so, we can develop fast convergence iterative algorithms with the errors between 10-10 and 10-11, upon comparing numerical solutions to exact ones.
The formation of a double-horn current profile is a challenging issue in the achievement of electron bunch with high peak current, especially for high-repetition-rate X-ray free-electron lasers ...(XFELs) where more nonlinear and intricate beam dynamics propagation is involved. Here, we propose to correct the nonlinear beam longitudinal phase space distortion in the photoinjector section with a dual-mode buncher. In combination with the evolutionary many-objective beam dynamics optimization, this method is shown to be effective in manipulating the longitudinal phase space at the injector exit. Furthermore, the formation of the current spike is avoided after the multi-stage charge density modulation and electron bunch with a peak current of 1.6 kA is achieved for 100-pC bunch charge. Start-to-end simulations based on the Shanghai high-repetition-rate XFEL and extreme light facility demonstrate that the proposed scheme can increase the FEL pulse energy by more than 3 times in a cascading operation of echo-enabled harmonic generation and high-gain harmonic generation. Moreover, this method can also be used for longitudinal phase space shaping of electron beams operating at a high repetition rate to meet the specific demands of different researches.
•Folding wing aircraft and offshore wind turbine are focused on.•An efficient dynamic simulation method is developed.•Experimental validation using wind tunnel was conducted.•Simulation and ...experiment were in good agreement.
A novel singularity-free, tuning-free, and reduced-order strain-based beam formulation is developed for analyzing slender multibody systems such as folding wing aircraft and offshore wind turbines that perform large rigid body motions and geometrically nonlinear deformations. Conventional linear deformation models are not suitable for the analysis, whereas the strain-based beam formulation has a potential to describe the geometrically nonlinear deformation efficiently using a small number of strain variables and a constant stiffness matrix obtained from a recursive equation. However, it suffers from singularity, penalty-coefficient tuning, and many variables when applied to multibody systems. This study addressed these problems by proposing joint parameters. Singularity-free joint parameters introduced in the recursive equation produce a novel velocity transformation that removes coefficient tuning and achieves model reduction. We demonstrate that the proposed method can perform a more stable multibody analysis compared to that using the conventional method. Further, we measured the strain of the folding wing during deployment in a wind tunnel at the Institute of Fluid Science, Tohoku University to validate the strain-based beam formulation with the proposed joint parameters. The strain of the proposed method is in good agreement with that of the wind tunnel experiment, wherein the folding wing performed multibody dynamic motion with geometrically nonlinear deformation.
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In this work we present a novel computational method for embedding arbitrary curved one-dimensional (1D) fibers into three-dimensional (3D) solid volumes, as e.g. in fiber-reinforced materials. The ...fibers are explicitly modeled with highly efficient 1D geometrically exact beam finite elements, based on various types of geometrically nonlinear beam theories. The surrounding solid volume is modeled with 3D continuum (solid) elements. An embedded mortar-type approach is employed to enforce the kinematic coupling constraints between the beam elements and solid elements on non-matching meshes. This allows for very flexible mesh generation and simple material modeling procedures in the solid, since it can be discretized without having to account for the reinforcements, while still being able to capture complex nonlinear effects due to the embedded fibers. Several numerical examples demonstrate the consistency, robustness and accuracy of the proposed method, as well as its applicability to rather complex fiber-reinforced structures of practical relevance.
A novel mathematical model for fiber-reinforced materials is proposed. It is based on a 1-dimensional beam model for the thin fiber structures, a flexible and general 3-dimensional elasticity model ...for the matrix and an overlapping domain decomposition approach. From a computational point of view, this is motivated by the fact that matrix and fibers can be easily meshed independently. Our main interest is in fiber-reinforced polymers where the Young modulus is quite different. Thus the modeling error from the overlapping approach is of no significance. The coupling conditions acknowledge both, the forces and the moments of the beam model and transfer them to the background material. A suitable static condensation procedure is applied to remove the beam balance equations. The condensed system then forms our starting point for a numerical approximation in terms of isogeometric analysis. The choice of our discrete basis functions of higher regularity is motivated by the fact, that as a result of the static condensation, we obtain second gradient terms in fiber direction. Eventually, a series of benchmark tests demonstrate the flexibility and robustness of the proposed methodology. As a proof-of-concept, we show that our new model is able to capture bending, torsion and shear dominated situations.
•We present a novel 1D–3D coupling to embed continuum degenerated beams into 3-dimensional solids.•We allow to transfer the mean force, couple stresses, shear and dilatation forces.•A static condensation procedure allows us to remove the degrees of freedom associated with the beams.•The static condensation results in a second gradient material model.•A series of tests demonstrates the flexibility as well as the accuracy of the proposed method.
This paper proposes a coupling scheme for isogeometric elements, which is valid for large rotations and displacements. Two elements can be coupled not only at interpolated control points but also ...inside the parametric domain of a NURBS patch. Furthermore, each cross section may be arbitrarily oriented in space. The formulation is applicable for all structural elements, where an orthogonal system of base vectors can be derived. An Euler–Bernoulli beam is used as an example in order to illustrate the demands on the coupling conditions in the proposed approach. Moreover, the conditions are chosen such that different types of joints, e.g. scissor joints, can be modeled and such that they are easy and fast to implement. The coupling is incorporated by an additional term in the Principle of Virtual Work which is here computed using a penalty approach. The Euler–Bernoulli beam is summarized in order to introduce the notations in this contribution. This is followed by the proposed coupling conditions in the weak form. Subsequently, alternatives for the coupling conditions are briefly introduced. Eventually, benchmark and demonstrator examples validate and illustrate the proposed coupling methodology.
In this paper, targeted energy transfer from a nonlinear continuous system to a nonlinear energy sink (NES) is investigated. For this purpose, the equation of a nonlinear beam with simply supported ...ends, on which the NES is attached, is derived using Rayleigh–Ritz method and the Lagrange equation. Then, parameters of the NES are optimized by both sensitivity analysis and particle swarm optimization (PSO) method. Analysis of the energy transfer between the nonlinear beam and the NES is presented, using the complexification-averaging method, too. Attaching an NES to a nonlinear continuous system and using the PSO method to obtain the optimized parameters of the NES is a new development, presented in this work. Also, here, more than one mode of the beam has been considered for analysis of energy transfer between the NES and different modes of the primary system.
The article is focused on a two‐dimensional geometrically nonlinear formulation of a Bernoulli beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is ...based on the integrated form of equilibrium equations, which are combined with the kinematic equations and generalized material equations, leading to a set of three first‐order differential equations. These equations are then discretized by finite differences and the boundary value problem is converted into an initial value problem using a technique inspired by the shooting method. Accuracy of the numerical approximation is conveniently increased by refining the integration scheme on the element level while the number of global degrees of freedom is kept constant, which leads to high computational efficiency. The element has been implemented into an open‐source finite element code. Numerical examples show a favorable comparison with standard beam elements formulated in the finite‐strain framework and with analytical solutions.
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