Fabian Bause

Transient modeling of ultrasonic guided waves in circular viscoelastic waveguides for inverse material characterization

In this contribution, we present an efficient approach for the transient and time-causal modeling of guided waves in viscoelastic cylindrical waveguides in the context of ultrasonic material characterization. We use the scaled boundary finite element method (SBFEM) for efficient computation of the phase velocity dispersion. Regarding the viscoelastic behavior of the materials under consideration, we propose a decomposition approach that considers the real-valued frequency dependence of the (visco-)elastic moduli and, separately, of their attenuation. The modal expansion approach is utilized to take the transmitting and receiving transducers into account and to propagate the excited waveguide modes through a waveguide of finite length. The effectiveness of the proposed simulation model is shown by comparison with a standard transient FEM simulation as well as simulation results based on the exact solution of the complex-valued viscoelastic guided wave problem. Two material models are discussed, namely the fractional Zener model and the anti-Zener model; we re-interpret the latter in terms of the Rayleigh damping model. Measurements are taken on a polypropylene sample and the proposed transient simulation model is used for inverse material characterization. The extracted material properties may then be used in computer-aided design of ultrasonic systems.

Messsystem zur Bestimmung akustischer Kenngrößen stark absorbierender, transversal isotroper Kunststoffe

Zusammenfassung Es wird ein wellenleiterbasierter Ansatz zur Bestimmung von Modellparametern für die numerische Simulation der Schallausbreitung in stark absorbierenden, transversal isotropen Kunststoffen vorgestellt. Aufbauend auf einer ersten strahlentheoretischen Schätzung wird innerhalb eines inversen Ansatzes eine multimodale wellentheoretische Simulation der Schallausbreitung im Wellenleiter realisiert. Abstract In this contribution we present a waveguide-based approach for the determination of highly absorbing, transversely isotropic polymers for numerical simulation purposes. Based on a multimodal simulation of wave propagation the directional as well as frequency dependent acoustic properties are computed within an inverse problem.

An improved mode-tracing algorithm to compute dispersion curves of acoustic waveguides

Semi-analytical approaches for the description of dispersion in acoustic waveguides are based on root finding in a characteristic function. A mode-tracing algorithm helps to find all solutions of this problem by consecutively bracketing single roots. In this contribution we present a multistage and adaptive mode-tracing algorithm, which uses an adaptive step size for the prediction of consecutive solutions as well as an adaptive estimation of the search space around these predictions. Furthermore we present a validation stage to ensure the correlation between consecutive solutions alias waveguide modes.

Time-causal material modeling in the simulation of guided waves in circular viscoelastic waveguides

For the description of linear viscoelasticity, the fractional Zener model may be used. Based on the spectral decomposition of the elasticity matrix as proposed by Theocaris, we generalize the one-dimensional analysis of the material model into three dimensions and discuss appropriate simplifications to reduce the amount of unknowns for the material description. Then, a decomposition approach that considers the real valued frequency dependence of the viscoelastic moduli and the real valued frequency dependence of their attenuation separately is proposed. The Scaled Boundary Finite Element Method is used for the efficient computation of the phase velocity dispersion and the modal wave fields given a frequency dependent but real valued viscoelasticity matrix. Utilizing the modal expansion approach, the transmitting and receiving transducer are taken into account to compute the modal amplitudes. Combining these modal amplitudes, the phase velocity dispersion and re-introducing the viscoelastic attenuation results in a transfer function of the viscoelastic waveguide including excitation and receiving conditions. The performance of the proposed simulation model is shown by comparison to measurements taken on a polypropylene sample.

Reliable computation of roots in analytical waveguide modeling using an interval-newton approach and algorithmic differentiation

For the modeling and simulation of wave propagation in geometrically simple waveguides such as plates or rods, one may employ the analytical global matrix method. That is, a certain (global) matrix depending on the two parameters wavenumber and frequency is built. Subsequently, one must calculate all parameter pairs within the domain of interest where the global matrix becomes singular. For this purpose, one could compute all roots of the determinant of the global matrix when the two parameters vary in the given intervals. This requirement to calculate all roots is actually the methods most concerning restriction. Previous approaches are based on so-called mode-tracers, which use the physical phenomenon that solutions, i.e., roots of the determinant of the global matrix, appear in a certain pattern, the waveguide modes, to limit the root-finding algorithms search space with respect to consecutive solutions. In some cases, these reductions of the search space yield only an incomplete set of solutions, because some roots may be missed as a result of uncertain predictions. Therefore, we propose replacement of the mode-tracer approach with a suitable version of an interval- Newton method. To apply this interval-based method, we extended the interval and derivative computation provided by a numerical computing environment such that corresponding information is also available for Bessel functions used in circular models of acoustic waveguides. We present numerical results for two different scenarios. First, a polymeric cylindrical waveguide is simulated, and second, we show simulation results of a one-sided fluid-loaded plate. For both scenarios, we compare results obtained with the proposed interval-Newton algorithm and commercial software.

Sensitivity study of signal characteristics for an inverse waveguide based approach of material characterization

A very promising approach for the ultrasonic identification of highly damping viscoelastic polymers has been proposed by Rautenberg [1]. He uses transmission measurements through hollow cylindrical shaped test samples which are modeled as waveguides. The measurement effect relies on multiple mode-conversions at the waveguides outer and inner boundaries and is evaluated based on an inverse approach. In this contribution we discuss different signal characteristics of the obtained dispersed signals with respect to their sensitivity to certain material parameters. Based on these sensitivities we propose a multiphase optimization scheme to increase the optimizations convergence.

Geführte akustische Wellen zur Flüssigkeitscharakterisierung

Zusammenfassung Das Spektrum akustischer Wellenleiter zur Flüssigkeitscharakterisierung reicht von der Seismologie und Geophysik mit Wellenleiterdimensionen von einigen km bis hin zur Prozessmesstechnik mit Sensordimensionen von wenigen mm. In diesem Beitrag wird ein phänomenologischer Weg zur Klassifizierung der Wellenleiter entwickelt, wobei stets die Oberflächenauslenkungen an der Wellenleitergrenze und die Anzahl der an der Wellenausbreitung beteiligten Moden Berücksichtigung finden. Im weiteren Verlauf werden Möglichkeiten zur Modellierung, Simulation und Messung multimodaler Wellenausbreitung im akustischen Wellenleiter gezeigt. Abstract This paper gives a survey on acoustic waveguides that are used for the measurement of properties of liquid. As guided acoustic waves range from the mm-scale to the km-scale, they are used in lots of scientific disciplines like seismology, geophysics, or process measurement engineering. A phenomenological way of classifying these waveguides will be developed, always considering the displacement characteristics of the waveguide´s boundary as well as single mode, multimode, or bulk mode operation. Later on, this article will focus on the modelling, simulation, and measurement of multimode wave propagation in acoustic waveguides.

Ultrasonic transmission measurements in the characterization of viscoelasticity utilizing polymeric waveguides

For the numerical simulation of acoustic wave propagation in (measurement) systems and their design, the use of reliable material models and material parameters is a central issue. Especially in polymers, acoustic material parameters cannot be evaluated based on quasistatically measured parameters, as are specified in data sheets by the manufacturers. In this work, a measurement method is presented which quantifies, for a given polymeric material sample, a complex-valued and frequency-dependent material model. A novel three-dimensional approach for modeling viscoelasticity is introduced. The material samples are designed as hollow cylindrical waveguides to account for the high damping characteristics of the polymers under test and to provide an axisymmetric structure for good performance of waveguide modeling and reproducible coupling conditions arising from the smaller coupling area in the experiment. Ultrasonic transmission measurements are carried out between the parallel faces of the sample. To account for the frequency dependency of the material properties, five different transducer pairs with ascending central frequency from 750 kHz to 2.5 MHz are used. After passing through the sample, each of the five received signals contains information on the material parameters which are determined in an inverse procedure. The solution of the inverse problem is carried out by iterative comparison of an innovative forward SBFEM-based simulations of the entire measurement system with the experimentally determined measurement data. For a given solution of the inverse problem, an estimate of the measurement uncertainty of each identified material parameter is calculated. Moreover, a second measurement setup, based on laser-acoustic excitation of Lamb modes in plate-shaped specimens, is presented. Using this setup, the identified material properties can be verified on samples with a varied geometry, but made from the same material.

Ultrasonic waveguide signal decomposition using the synchrosqueezed wavelet transform for modal group delay computation

Due to the modal behavior of geometrically bounded media, ultrasonic guided waves propagate in waveguides as a combination of multiple dispersive wave packets, which can be simulated as a PDE-problem. Given an excitation in time and space, multiple eigen-modes derived from solving the PDE may propagate each with different dispersion characteristics and weight. Considering a broad-band pulse exciting from one side of a hollow cylindrical waveguide, the received signal at the other side consists of all propagating eigen-modes that can be considered approximately as the narrow band signals. The synchrosqueezed wavelet transform (SWT) is employed to sharpen the time-frequency representation (TFR) of the received waveguide signal. Using a ridge detection algorithm, we successively separate the synchrosqueezed TFR into several narrow band TFRs which can be identified as oscillatory components with time-varying frequency. Then those separated TFRs are reconstructed as narrow band signals using the inverse SWT. Based on an analytical model of the waveguide, we observe that the decomposed signals are similar to those dominant eigen-modes simulated above. Moreover, also the group delay and, therefore, the group velocity of each decomposed signal can be estimated well. This is of high interest when analyzing the characteristic of a given waveguide, such as acoustical property measurements or non-destructive testing.

Viskoelastizität und Anisotropie von Kunststoffen: Ultraschallbasierte Methoden zur Materialparameterbestimmung

Zusammenfassung In diesem Beitrag werden verschiedene Aspekte der ultraschallbasierten Messtechnik hinsichtlich der Materialparameterbestimmung an viskoelastischen Materialien behandelt. Zunächst wird ein viskoelastisches Materialmodell unter Berücksichtigung von Anisotropie und Kausalität erarbeitet. Nachfolgend werden zwei verschiedene Verfahren zur Charakterisierung von Materialparametern anhand von geführten Ultraschallwellen in zylindrischen und plattenförmigen Strukturen vorgestellt sowie Vor- und Nachteile diskutiert. Dabei wird ebenso auf die Betrachtung von Materialalterung eingegangen. Beispielhaft untersucht werden thermoplastische Materialien wie Polypropylen und Polyamid 6. Zur Charakterisierung starker Anisotropie wird auch auf glasfaserverstärkte Plattenstrukturen mit thermoplastischer Matrix eingegangen.