A Multiwavelength Dynamical State Analysis of ACT-CL J0019.6+0336

In our study, we show a multiwavelength view of ACT-CL J0019.6+0336 (which hosts a radio halo), to investigate the cluster dynamics, morphology, and ICM. We use a combination of XMM-Newton images, Dark Energy Survey (DES) imaging and photometry, SDSS spectroscopic information, and 1.16 GHz MeerKAT data to study the cluster properties. Various X-ray and optical morphology parameters are calculated to investigate the level of disturbance. We find disturbances in two X-ray parameters and the optical density map shows elongated and axisymmetric structures with the main cluster component southeast of the cluster centre and another component northwest of the cluster centre. We also find a BCG offset of ∼950 km/s from the mean velocity of the cluster, and a discrepancy between the SZ mass, X-ray mass, and dynamical mass (MX,500 and MSZ,500 lies >3σ away from Mdyn,500), showing that J0019 is a merging cluster and probably in a post-merging phase.

Curvature effects and radial homoclinic snaking

In this work, we revisit some general results on the dynamics of circular fronts between homogeneous states and the formation of localized structures in two dimensions (2D). We show how the bifurcation diagram of axisymmetric structures localized in radius fits within the framework of collapsed homoclinic snaking. In 2D, owing to curvature effects, the collapse of the snaking structure follows a different scaling that is determined by the so-called nucleation radius. Moreover, in the case of fronts between two symmetry-related states, the precise point in parameter space to which radial snaking collapses is not a ‘Maxwell’ point but is determined by the curvature-driven dynamics only. In this case, the snaking collapses to a ‘zero surface tension’ point. Near this point, the breaking of symmetry between the homogeneous states tilts the snaking diagram. A different scaling law is found for the collapse of the snaking curve in each case. Curvature effects on axisymmetric localized states with internal structure are also discussed, as are cellular structures separated from a homogeneous state by a circular front. While some of these results are well understood in terms of curvature-driven dynamics and front interactions, a proper mathematical description in terms of homoclinic trajectories in a radial spatial dynamics description is lacking.

Topology Optimization for Additively Manufactured Self-Supporting Axisymmetric Structures

This paper discusses the design of axisymmetric structures with self-supporting features that can be additively manufactured without requiring internal support structures. This is motivated by wire-fed additive manufacturing processes, many of which can fabricate designs with enclosed pores that inherently exist in many axisymmetric structures, such as double walled pressure vessels. Although enclosed pores are possible, features that rise at shallow angles from the build plate typically cannot be fabricated without the use of support structures, which require removal and thus are unfavorable in such applications. In this paper, an overhang constraint is applied to ensure that all designed features rise at a designer-prescribed self-supporting angle to eliminate the need for such support structures. This is achieved by coupling the projection-based overhang constraint approach with topology optimization and axisymmetric finite elements whose stiffness is interpolated using Solid Isotropic Material with Penalization (SIMP). Gradients are computed with the adjoint method and the Method of Moving Asymptotes (MMA) is employed as the gradient-based optimizer. Two numerical examples related to a canonical pressure vessel and an optical mirror support structure are used to demonstrate the approach. Solutions are shown to satisfy minimum feature size requirements and designer-prescribed (process dependent) overhang constraint angles, while providing clear and crisp representations of topology. As observed in past works on overhang constraints, a clear trade-off is illustrated between the magnitude of the overhang constraint angle and the structural performance (mass or stiffness), with more strict requirements producing designs with lower performance.

Mode Shape Description and Model Updating of Axisymmetric Structures Using Radial Tchebichef Moment Descriptors

A novel approach for mode shape feature extraction and model updating of axisymmetric structures based on radial Tchebichef moment (RTM) descriptors is proposed in this study. The mode shape features extracted by RTM descriptors can effectively compress the full-field modal vibration data and retain the most important information. The reconstruction of mode shapes using RTM descriptors can accurately describe the mode shapes, and the simulation shows that the RTM function is superior to Zernike moment function in terms of its mathematical properties and its shape reconstruction ability. In addition, the proposed modal correlation coefficient of the RTM amplitude can overcome the main disadvantage of using the modal assurance criterion (MAC), which has difficulty in identifying double or close modes of symmetric structures. Furthermore, the model updating of axisymmetric structures based on RTM descriptors appears to be more efficient and effective than the normal model updating method directly using modal vibration data, avoids manipulating large amounts of mode shape data, and speeds up the convergence of updating parameters. The RTM descriptors used in correlation analysis and model updating are demonstrated with a cover of an aeroengine rig. The frequency deviation between the test and the FE model was reduced from 17.13% to 1.23% for the first 13 modes via the model updating process. It verified the potential to industrial application with the proposed method.

Dynamics of high-rise structures taking into account the viscoelastic properties of the material

The article deals with forced vibrations of a high-rise axisymmetric structure, represented as a viscoelastic beam of an annular section with a variable slope of the generatrices and variable thickness. The research was conducted to analyze the behavior of a high-rise structure for various kinematic effects. The task is to determine the displacements of the points of a high-rise structure at different time points under different kinematic effects. The methods were developed and a computer program was built; forced vibrations of high-rise axisymmetric structures under various kinematic actions, considering viscoelastic properties of the material, were investigated in linear, nonlinear, and viscoelastic formulations. The study of the dynamic behavior of a high-rise structure, taking into account the nonlinear and dissipative properties (different in nature) of the material, shows that the combined consideration of all these properties brings the resulting pattern closer to the one observed in reality. That is, the amplitude of the structure’s oscillations does not grow infinitely, but gradually decreases over time, and the maximum possible consideration of nonlinear and dissipative properties leads to the fastest damping of oscillations.

High-order three-scale computational method for elastic behavior analysis and strength prediction of axisymmetric composite structures with multiple spatial scales

A novel high-order three-scale (HOTS) computational method for elastic behavior analysis and strength prediction of axisymmetric composite structures with multiple spatial scales is developed in this paper. The multiple heterogeneities of axisymmetric composite structures we investigated are taken into account by periodic distributions of representative unit cells on the mesoscale and microscale. First, the new micro–meso–macro coupled HOTS computational model for elastic problems of axisymmetric composite structures is established based on multiscale asymptotic analysis, which breaks through the traditional multiscale assumptions and includes three main components. Two classes of mesoscopic and microscopic auxiliary cell functions are constructed on the mesoscale and microscale, respectively. The macroscopic homogenization problems are defined on global axisymmetric structures by twice up-scaling procedures from microscale to mesoscale and then from mesoscale to macroscale. Moreover, the asymptotic HOTS solutions are constructed for approximating multiscale elastic problems of axisymmetric structures and the numerical accuracy analysis of the HOTS solutions is given in detail. Then, the strength prediction formulas for axisymmetric composite structures with multiple spatial scales are presented based on the high-accuracy elastic behavior analysis from the proposed HOTS computational model. Furthermore, the corresponding HOTS numerical algorithm based on the finite element method (FEM) is presented for analyzing the mechanical behaviors and predicting the strength of axisymmetric composite structures with multiple spatial scales in detail. Finally, some numerical examples are reported to verify the feasibility and effectiveness of the proposed HOTS computational method. In this study, a unified three-scale computational framework is offered, which enables the simulation of mechanical behaviors of axisymmetric composite structures with multiple spatial scales.