Note: [255] Reference LCH-CONF-1998-009 Record created on 2007-04-24, modified on 2016-08-08

The scaled boundary finite-element method – a primer: derivations

Simulation of elastic guided waves interacting with defects in arbitrarily long structures using the Scaled Boundary Finite Element Method

Isogeometric analysis enhanced by the scaled boundary finite element method

A numerical study of the effects of the T-shaped baffles on liquid sloshing in horizontal elliptical tanks

Piezoelectric materials characterization is a challenging problem involving physical concepts, electrical and mechanical measurements and numerical optimization techniques. Piezoelectric ceramics such as Lead Zirconate Titanate (PZT) belong to the 6 mm symmetry class, which requires five elastic, three piezoelectric and two dielectric constants to fully represent the material properties. If losses are considered, the material properties can be represented by complex numbers. In this case, 20 independent material constants are required to obtain the full model. Several numerical methods have been used to adjust the theoretical models to the experimental results. The continuous improvement of the computer processing ability has allowed the use of a specific numerical method, the Finite Element Method (FEM), to iteratively solve the problem of finding the piezoelectric constants. This review presents the recent advances in the numerical characterization of 6 mm piezoelectric materials from experimental electrical impedance curves. The basic strategy consists in measuring the electrical impedance curve of a piezoelectric disk, and then combining the Finite Element Method with an iterative algorithm to find a set of material properties that minimizes the difference between the numerical impedance curve and the experimental one. Different methods to validate the results are also discussed. Examples of characterization of some common piezoelectric ceramics are presented to show the practical application of the described methods.

Numerical Characterization of Piezoceramics Using Resonance Curves.

On the computation of dispersion curves for axisymmetric elastic waveguides using the Scaled Boundary Finite Element Method

. In the non-destructive determination of material properties, the utilization of ultrasound has proven to be a viable tool. In the presented paper, a laser is used to create broadband acoustic waves in plate-shaped specimens by applying the photoacoustic effect. The waves are detected using a purpose-built ultrasonic transducer that is based on piezoceramics instead of the commonly used piezoelectric polymer films. This new transducer concept allows for detection of ultrasonic waves up to 10 MHz with high sensitivity, thereby allowing the characterization of highly damping materials such as polymers. The recorded data are analysed using different methods to obtain information on the propagation modes transmitted along the specimen. In an inverse procedure, the gained results are compared to simulations, yielding approximations for the specimen's material properties.

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Determination of the material properties of polymers using laser-generated broadband ultrasound

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.

https://iopscience.iop.org/article/10.1088/0957-0233/26/9/095602/pdf

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

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.

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

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.

http://iopscience.iop.org/article/10.1088/0957-0233/27/10/105601/pdf

Fabian Bause

Papers

On the computation of dispersion curves for axisymmetric elastic waveguides using the Scaled Boundary Finite Element Method

Determination of the material properties of polymers using laser-generated broadband ultrasound

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

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

Ultrasonic transmission measurements in the characterization of viscoelasticity utilizing polymeric waveguides