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We present a method to extract monopole and dipole polarizability from experimental measurements of two-dimensional acoustic meta-atoms. In contrast to extraction from numerical results, this enables all second-order effects and uncertainties in material properties to be accounted for. We apply the technique to 3D-printed labyrinthine meta-atoms of a variety of geometries. We show that the polarizability of structures with a shorter acoustic path length agrees well with numerical results. However, those with longer path lengths suffer strong additional damping, which we attribute to the strong viscous and thermal losses in narrow channels.
Application of a Krylov subspace method for an efficient solution of acoustic transfer functions
(2021)
Solving acoustic radiation problems, arising from systems including fluid–structure interaction, is of interest in many engineering applications. Computing frequency response functions over a large frequency range is a concern in such applications. A method which solves the Helmholtz equation for multiple frequencies in one step is the matrix-Padé-via-Lanczos connection for unsymmetric systems, as presented by Wagner et al. [1]. The present work is based on Ref. [1] and presents a method for efficiently computing frequency responses over a frequency range for coupled structural-acoustic problems, where the structure and the acoustic near field are discretized with finite elements and an analytical Dirichlet-to-Neumann map approximates the far field. The method is based on a Krylov-subspace projection technique which derives a matrix-valued Padé approximation for a restricted area in the near field and the pressure field on a spherical boundary. On the spherical boundary, where the finite domain is truncated, the non-local modified Dirichlet-to-Neumann operator is applied as a low-rank update matrix. The present contribution extends this method and incorporates new techniques for a more stable model reduction through the Lanczos algorithm and a novel weighted adaptive windowing technique. Further, structural damping is incorporated, for computing the acoustic radiation of a harmonically excited plate. These computed results are compared with acoustic measurements in an anechoic chamber and verified with computational results obtained with a commercial code that uses the perfectly matched layer method.
Finite element simulation of blankholder’s lift-off in a deep drawing tool using Abaqus/Standard
(2015)
In the deep drawing tools for forming car body parts, heavy blankholders are used to prevent buckling and wrinkling of the blank. During each press cycle, those large masses need to be lifted, raising thereby the structural dynamic load on the deep drawing tool and on the press. Therefore a detailed knowledge about the blankholder’s lift-off event is essential for an accurate and robust design of forming tools. In this paper, a dynamic finite element method (FEM) simulation of a blankholder’s lift-off in a selected automotive deep drawing tool is presented enabling identification of regions of critical stresses. The FEM model is built within the Abaqus/CAE environment and solved with Abaqus/Standard. Each dynamic analysis is preceded by a static analysis where the gravity load is applied and the lifting bolts are pre-stressed. A special emphasis is put on modeling the elastomer dampers, which are installed between lifting bolts and the blankholder to avoid hard impacts during the lift-off event. Those dampers are modelled using a hyperelastic material with hysteresis. In addition, an experimental validation of a blankholder’s vibration under operating loading was carried out. The simulation results are in good agreement with the measurements.
This paper presents experimental fatigue tests on specially shaped specimens made from quenched and tempered steel 42CrMoS4 and nodular cast iron EN-GJS-600-3. The specimens are geometrically designed to resemble actual subcomponents of forming and cutting dies for sheet metal manufacturing. These subcomponents have failed in the past.Experiments are carried out using a fictive load-time function, which is a modification of an actually measured load curve and has variable mean and amplitude values. This first test series serves as a general validation of a subsequent fatigue analysis. A second test series is carried out with constant mean and amplitude values with a load ratio 𝑅≈0. Here, the load frequencies in the individual test runs are varied between f = 5 Hz and f = 45 Hz in order to investigate the influence of the frequency. Both series are performed on a servo-hydraulic testing machine.The experimental data is then statistically evaluated. The values for the scatter correlate with data from the literature. The data from the test series with the fictive load-time function can thus be used for subsequent validation of a fatigue calculation, which will be addressed in a future publication. Most significant are the findings from the second series of experiments with varied load frequencies, as a significant frequency influence could be detected. Furthermore, the hardening and softening behavior under cyclic loading and the fracture behavior of the materials are analyzed and compared with data from the literature.
In order to achieve the energy and efficiency goals in modern automotive press shops, press systems with increasingly high stroke rates are being implemented (Meinhardt in proceedings of ACI forming in car body engineering. Bad Nauheim, Germany 2012). As a side effect, the structural dynamic loads on the press and especially on the forming tool increase. Hence, to design reliable and withstanding forming tools, a detailed knowledge of the vibrations and resulting critical loads is essential. In this paper, the main focus is put on the vibration of the blankholder—the heaviest moving component in the forming tool. To predict those vibrations, a coupled multibody-finite element simulation (MBS-FEM) is conducted, which combines rigid and elastic modeling approaches. Also, an experimental validation of the blankholder vibration under operational load is carried out. To compare the numerical and experimental results—both in time and frequency domain—an 1/3-octave analysis of a blankholder’s vibrational speed is performed. The test measurements agree well with the MBS-FEM simulation.
Because of increased stroke rates the loads on forming tools increase too. To ensure a save design of components, durability analyses are intended. For this, simulation results from FE analyses are necessary. Therefore, it is desirable to use elements with quadratic function, because of a good stress approximation.The goal of the described investigation is to show if calculation results created by LS-DYNA [1] can be used for durability analyses. Especially the use of quadratic elements is investigated. For the evaluation, on the one hand explicit FE analyses of a special durability test are carried out. These analyses are validated by available test data. To create results for later durability analyses further FE analyses with implicit time discretisation are carried out. In this paper results of the investigations are presented and evaluated critically.
Effiziente Methode zur Bestimmung von dynamischen strukturellen Belastungen in Großpresswerkzeugen
(2016)
To improve efficiency in automotive press shops, press systems with increasingly high stroke rates are beingimplemented, raising thereby the structural dynamic load on the press and especially on the forming tool. Adetailed knowledge of the vibrations and resulting critical loads is thus essential for accurate and reliable de-signs of forming tools. In this paper, multibody simulation (MBS) of a selected automotive tool is presentedenabling the identification of the vibration of its components. Starting from a pure rigid modelling approach,the MBS model is extended by adding finite element (FE) component to allow extra flexibility in the sys-tem. As an example, a detailed vibrational analysis - both in time and frequency domain - is performed ona blankholder. Also an experimental validation of a blankholder vibration under operational load is carriedout, with test signal data gained by piezoelectric accelerometers.