Determining periodic orbits via nonlinear filtering and recurrence spectra in the presence of noise

© 2017 The Authors. Published by Elsevier Ltd. In nonlinear dynamical systems the determination of stable and unstable periodic orbits as part of phase space prediction is problematic in particular if perturbed by noise. Fourier spectra of the time series or its autocorrelation function have shown to be of little use if the dynamic process is not strictly wide-sense stationary or if it is nonlinear. To locate unstable periodic orbits of a chaotic attractor in phase space the least stable eigenvalue can be determined by approximating locally the trajectory via linearisation. This approximation can be achieved by employing a Gaussian kernel estimator and minimising the summed up distances of the measured time series i.e. its estimated trajectory (e.g. via Levenberg-Marquardt). Noise poses a significant problem here. The application of the Wiener-Khinchin theorem to the time series in combination with recurrence plots, i.e. the Fourier transform of the recurrence times or rates, has been shown capable of detecting higher order dynamics (period-2 or period-3 orbits), which can fail using classical FouRiER-based methods. However little is known about its parameter sensitivity, e.g. with respect to the time delay, the embedding dimension or perturbations. Here we provide preliminary results on the application of the recurrence time spectrum by analysing the Hénon and the Rössler attractor. Results indicate that the combination of recurrence time spectra with a nonlinearly filtered plot of return times is able to estimate the unstable periodic orbits. Owing to the use of recurrence plot based measures the analysis is more robust against noise than the conventional Fourier transform

A platform for benchmark cases in computational acoustics

Solutions to the partial differential equations that describe acoustic problems can be found by analytical, numerical and experimental techniques. Within arbitrary domains and for arbitrary initial and boundary conditions, all solution techniques require certain assumptions and simplifications. It is difficult to estimate the precision of a solution technique. Due to the lack of a common process to quantify and report the performance of the solution technique, a variety of ways exists to discuss the results with the scientific community. Moreover, the absence of general reference results does hamper the validation of newly developed techniques. Over the years many researchers in the field of computational acoustics have therefore expressed the need and wish to have available common benchmark cases. This contribution is intended to be the start of a long term project, about deploying benchmarks in the entire field of computational acoustics. The platform is a web-based database, where cases and results can be submitted by all researchers and are openly available. Long-term maintenance of this platform is ensured. As an example of good practice, this paper presents a framework for the field of linear acoustic. Within this field, different categories are defined – as bounded or unbounded problems, scattering or radiating problems and time-domain as well as frequency-domain problems – and a structure is proposed how to describe a benchmark case. Furthermore, a way of reporting on the used solution technique and its result is suggested. Three problems have been defined that demonstrate how the benchmark cases are intended to be used

Research and development of an air-puff excitation system for lightweight structures

© 2019 International Group of Operational Modal Analysis. Lightweight, thin-walled structures appear in numerous engineering and natural structures. Due to their sensitivity, vibration excitation by, now traditional, contacting techniques, such as modally-tuned impact hammers or electrodynamic shakers, to investigate their dynamics is challenging since it typically adds substantial mass and/or stiffness at the excitation location. The research presented in this article, therefore, is intended to yield a system for the non-contact excitation of thin-walled structures through small, controlled blasts of air. An air-puff system, consisting of two fast-acting solenoid-controlled valves, a small air outlet nozzle and bespoke control software with a programmable valve control sequence, is researched and developed. The excitation impulse characteristics are investigated experimentally and described in detail for varying input control parameters. Ultimately, suitability of the system for the excitation of thin-walled structures is explored, for both a 3D-printed micro-satellite panel and a natural bee honeycomb, with promising results when compared to that of an impact hammer

Measuring monopole and dipole polarizability of acoustic meta-atoms

© 2018 Author(s). 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

Acoustic meta-atom with experimentally verified maximum Willis coupling

© 2019, The Author(s). Acoustic metamaterials are structures with exotic acoustic properties, with promising applications in acoustic beam steering, focusing, impedance matching, absorption and isolation. Recent work has shown that the efficiency of many acoustic metamaterials can be enhanced by controlling an additional parameter known as Willis coupling, which is analogous to bianisotropy in electromagnetic metamaterials. The magnitude of Willis coupling in a passive acoustic meta-atom has been shown theoretically to have an upper limit, however the feasibility of reaching this limit has not been experimentally investigated. Here we introduce a meta-atom with Willis coupling which closely approaches this theoretical limit, that is much simpler and less prone to thermo-viscous losses than previously reported structures. We perform two-dimensional experiments to measure the strong Willis coupling, supported by numerical calculations. Our meta-atom geometry is readily modeled analytically, enabling the strength of Willis coupling and its peak frequency to be easily controlled

Matching experimental and three dimensional numerical models for structural vibration problems with uncertainties

© 2017 The Author(s) The simulation model which examines the dynamic behavior of real structures needs to address the impact of uncertainty in both geometry and material parameters. This article investigates three-dimensional finite element models for structural dynamics problems with respect to both model and parameter uncertainties. The parameter uncertainties are determined via laboratory measurements on several beam-like samples. The parameters are then considered as random variables to the finite element model for exploring the uncertainty effects on the quality of the model outputs, i.e. natural frequencies. The accuracy of the output predictions from the model is compared with the experimental results. To this end, the non-contact experimental modal analysis is conducted to identify the natural frequency of the samples. The results show a good agreement compared with experimental data. Furthermore, it is demonstrated that geometrical uncertainties have more influence on the natural frequencies compared to material parameters and material uncertainties are about two times higher than geometrical uncertainties. This gives valuable insights for improving the finite element model due to various parameter ranges required in a modeling process involving uncertainty

Acoustic metamaterial capsule for reduction of stage machinery noise

Noise mitigation of stage machinery can be quite demanding and requires innovative solutions. In this work we propose an acoustic metamaterial capsule to reduce the noise emission of several stage machinery drive trains, while still allowing the ventilation required for cooling. The metamaterial capsule consists of c-shape meta atoms, which have a simple structure that facilitates manufacturing. We design, simulate, manufacture, and experimentally validate two different metamaterial capsules, which utilize an ultra-sparse and air-permeable reflective meta-grating. Both designs demonstrate transmission loss peaks that effectively suppress gear mesh noise or other narrow band noise sources. The ventilation by natural convection was numerically verified, and was shown to give adequate cooling, whereas a conventional sound capsule would lead to overheating. The noise spectra of three common stage machinery drive trains are numerically modelled, enabling us to design meta-gratings and determine their noise suppression performance. The results fulfill the stringent stage machinery noise limits, highlighting the benefit of using metamaterial capsule of simple c-shape structure

Numerical analysis of sound radiation from rotating discs

The analysis of sound radiation from rotating elastic discs, e.g. saw blades, is an interesting research topic. Especially for people who work in the vicinity of such machines, health related issues with respect to noise exposure levels gain more and more awareness. Therefore, the industry is faced with the challenge of developing quieter products in order to improve the working environment and to extend the time a worker can use these tools before a harmful situation arises. Moreover, less noise emission means less energy consumption and therefore a higher productivity. In this paper, the authors investigate the sound radiation from a rotating disc where the sound power is used as a global measure for the acoustic performance. Different methods for calculating the sound power of a spinning saw blade are compared. These are a fully coupled finite element approach, a hybrid finite element/boundary element approach, a simplified form of the Rayleigh integral known as the lumped parameter model, and the equivalent radiated sound power. The results show good agreement between the costly full models and those utilizing approximation methods which can save remarkable computational costs. The proposed frame can be used in optimization procedures for developing quieter saw blades and other rotating discs. Furthermore, the paper discusses mode splitting which is a well-known phenomenon for rotating machinery. For this, the results of sound radiation are investigated with respect to the question whether mode splitting is actually audible