arXiv subjects

Elke Deckers

Publications and source records attributed to Elke Deckers.

7 recordsLinked to original sources

arXiv2026

Mapping locally nondominated curves in multiobjective topology optimization of compliance and volume

This paper studies the nondominated set for topology optimization of compliance and volume. In the multiobjective topology optimization literature, scalarization is a popular method to approximate this set, which is better known as the Pareto frontier. However, previous work indicates that the pointwise approximation obtained by scalarization obfuscates its underlying mathematical structure: under an imposed length scale, it consists of locally nondominated curve segments. To investigate this structure, the paper uses a simple methodology to (i) generate local optima with a tightly controlled topology and (ii) use continuation to extend these points to locally nondominated curves. The paper then performs two rounds of numerical experiments. The first round applies the methodology to several cantilever examples. This leads to novel insights regarding topological complexity and symmetry and confirms prior conclusions regarding continuity, smoothness and convexity. The second round investigates two numerical instabilities: (i) a lack of uniqueness and (ii) discontinuities of the locally nondominated curves. The former is linked to an observed flatness of the optimization landscape, whereas the latter is attributed to branch splitting and linked to bifurcation theory. Namely, we classify these discontinuities as higher-dimensional analogues of the subcritical, symmetry-breaking pitchfork bifurcation. The paper concludes with suggestions for future research to address these features of the multiobjective optimization landscape.

math.OC↗

arXiv2026

Continuation strategies to mitigate convergence to low-performing local optima in topology optimization of sound transmission loss

Dynamic topology optimization problems often suffer from convergence to low-performing local optima. This typically results in stiff designs that do not exploit dynamical phenomena such as antiresonance and decoupling. To obtain better designs, researchers often repeat their optimizations with different initial guesses. However, such reruns are computationally expensive and the required number is unknown. To quantify this problem, random initial guesses are sampled and tested for different frequencies on two case studies: (1) dynamic compliance minimization of a reinforced cantilever, which exhibits poor optima for driving frequencies below the first natural frequency, and (2) sound transmission loss maximization of a sandwich panel, which additionally sees a strong tendency toward low-performing optima at high frequencies. To address this issue, the study first divides techniques to reduce the needed number of reruns into four categories: global optimization, exclusion, relaxation, and frequency shift methods. For the latter three, continuation strategies are proposed, illustrated, evaluated and compared on the sound transmission loss case, using Monte Carlo sampling to estimate success rates. All strategies show measurable benefits and trade-offs. To support broader applicability, the study concludes with practical guidelines for dealing with convergence to poor local optima in dynamic topology optimization.

math.OC↗

arXiv2026

Effect of introducing viscoelastic polyurethane on the dispersion and vibration isolation efficiency of chiral phononic crystals

Phononic crystals, a sequence of masses and (damped) springs, are being used more and more in practical applications, exploiting Bragg bandgaps to attenuate vibration transmission in a wide frequency range. In particular, chiral phononic crystals have demonstrated their ability to achieve low frequency bandgaps while maintaining a high static stiffness, and thus load bearing capacities. However, tuning of the bandgap frequencies is non-trivial because of their complex geometry. In this paper, viscoelastic inserts between the masses of the chain are introduced to improve the tunability of the crystal and take advantage of viscous damping. Modeling true viscoelasticity requires the implementation of frequency-dependent material properties, which is introduced in this work both for dispersion curve calculation and for harmonic force transmission simulations. As a real-world example, the intricate frequency-dependency of polyurethane is studied by examining the influence of four fractional derivative model parameters, which define the storage modulus and loss factor. The calculated dynamic force transmissibility of the phononic crystal is compared to classical, single-layer, isolation solutions. The results show that high viscous damping does not negatively affect the bandgap efficiency, which is a major advantage over resilient layer isolators where damping deteriorates the isolation properties. To validate the models, three crystals with different viscoelastic material properties in terms of stiffness and damping are manufactured and the measured force transmissibility is successfully compared to the numerical models.

physics.app-ph↗

arXiv2025

Practical implementation of a chiral phononic crystal demonstrator with ultra-low frequency bandgap

The use of phononic crystals for vibration attenuation and isolation has been widely studied, showing that the attenuation frequency range depends on their mass and stiffness. The concepts of chirality and tacticity have been introduced into classical phononic crystals to enrich the dynamics of the mass elements and thereby achieve lower frequency ranges with high vibration attenuation. Although these concepts have demonstrated their effectiveness on lab-scale crystals, their implementation in industrial applications is still rare. Chiral phononic crystals require a complex geometry that complicates their manufacturing. Existing examples require to be fabricated by 3D printing, making them expensive to build on a large scale for demonstration purposes or in-situ applications. In this study, we redefine a chiral phononic crystal design for translational-rotational coupling in order to enable its manufacturability using exclusively conventional processes. We then investigate the design space of these newly designed phononic crystals, using a simplified unit cell FEM model that minimizes computation time. A parametric study is conducted to investigate the crystal's tunability by modifying the dimensions of the chiral links between the masses. A large crystal with ultra-low frequency range attenuation -- starting at 60~Hz -- is then designed, with the aim to demonstrate the influence of the crystal's tacticity on the vibration isolation by hand sensing. A crystal composed of 2 unit cells is manufactured and its measured transfer function is compared with numerical predictions, thus highlighting the disparities between the behavior of the structure under real-life and ideal excitation conditions.

physics.app-ph↗

arXiv2024

Denoising of photogrammetric dummy head ear point clouds for individual Head-Related Transfer Functions computation

Individual Head-Related Transfer Functions (HRTFs), crucial for realistic virtual audio rendering, can be efficiently numerically computed from precise three-dimensional head and ear scans. While photogrammetry scanning is promising, it generally lacks accuracy, leading to HRTFs showing significant perceptual deviation from reference data, mainly due to scanning errors affecting the most occluded pinna structures. This paper examines the application of Deep Neural Networks (DNNs) for denoising photogrammetric ear scans. Several DNNs, fine-tuned on pinna samples corrupted with synthetic error modelled to mimic that observed in photogrammetric dummy head scans, are tested and benchmarked against a classical denoising method. One DNN is further modified and retrained to enhance its denoising performance. The comparison of HRTFs derived from original and denoised scans against reference data shows that the best-performing DNN marginally reduces the deviation of photogrammetric dummy head HRTFs to levels closer to accurately measured ones. Additionally, correlation analysis between geometric and HRTF metrics, computed on the scanned point clouds and their corresponding HRTFs, is used to identify key measures for evaluating the deviation between target and reference scans. These findings are expected to guide the selection of relevant loss functions and foster improvements in this and similar DNN models.

eess.AS↗

arXiv2024

A guide to numerical dispersion curve calculations: explanation, interpretation and basic Matlab code

Dispersion diagrams play a crucial role in examining, analyzing and designing wave propagation in periodic structures. Despite their ubiquity and current research interest, introductory papers and reference scripting tailored to novel researchers in the field are lacking. This paper aims to address this gap, by presenting a comprehensive educational resource for researchers starting in the field of periodic structures and more specifically on the study of dispersion relations captured by dispersion surfaces or curves in dispersion diagrams. The objective is twofold. A first objective is to give a detailed explanation of dispersion diagrams, with graphical illustrations. Secondly, a documented Matlab code is provided to compute dispersion curves of 3D structures with 2D periodicity using the so-called inverse approach. These dispersion curves are obtained with numerical simulations using the finite element method. The code is written for elastic wave propagation and orthogonal periodicity directions, but can be extended to other types of linear wave propagation, non-orthogonal periodicity directions or 1D and 3D periodicity. The aim of this code is to serve as a starting point for novice researchers in the field, to facilitate their understanding of different aspects of dispersion diagrams and serve as a stepping stone in their future research.

physics.app-ph↗

arXiv2022

Time integration of finite element models with nonlinear frequency dependencies

The analysis of sound and vibrations is often performed in the frequency domain, implying the assumption of steady-state behaviour and time-harmonic excitation. External excitations, however, may be transient rather than time-harmonic, requiring time-domain analysis. Some material properties, e.g.\ often used to represent for damping treatments, are still described in the frequency domain, which complicates simulation in time. In this paper, we present a method for the linearization of finite element models with nonlinear frequency dependencies. The linearization relies on the rational approximation of the finite element matrices by the AAA method. We introduce the Extended AAA method, which is classical AAA combined with a degree two polynomial term to capture the second order behaviour of the models. A filtering step is added for removing unstable poles.

math.NA↗