Measuring monopole and dipole polarizability of acoustic meta-atoms

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 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

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

Solving Galbrun’s Equation with a Discontinuous galerkin Finite Element Method

© S. Hirzel Verlag · EAA Over many years, scientists and engineers have developed a broad variety of mathematical formulations to investigate the propagation and interactions with flow of flow-induced noise in early-stage of product design and development. Beside established theories such as the linearized Euler equations (LEE), the linearized Navier–Stokes equations (LNSE) and the acoustic perturbation equations (APE) which are described in an Eulerian framework, Galbrun utilized a mixed Lagrange–Eulerian framework to reduce the number of unknowns by representing perturbations by means of particle displacement only. Despite the advantages of fewer degrees of freedom and the reduced effort to solve the system equations, a computational approach using standard continuous finite element methods (FEM) suffers from instabilities called spurious modes that pollute the solution. In this work, the authors employ a discontinuous Galerkin approach to overcome the difficulties related to spurious modes while solving Galbrun’s equation in a mixed and pure displacement based formulation. The results achieved with the proposed approach are compared with results from previous attempts to solve Galbrun’s equation. The numerical determination of acoustic modes and the identification of vortical modes is discussed. Furthermore, case studies for a lined-duct and an annulus supporting a rotating shear-flow are investigated