Jens Prager

The simulation of Lamb waves in a cracked plate using the scaled boundary finite element method

The scaled boundary finite element method is applied to the simulation of Lamb waves for ultrasonic testing applications. With this method, the general elastodynamic problem is solved, while only the boundary of the domain under consideration has to be discretized. The reflection of the fundamental Lamb wave modes from cracks of different geometry in a steel plate is modeled. A test problem is compared with commercial finite element software, showing the efficiency and convergence of the scaled boundary finite element method. A special formulation of this method is utilized to calculate dispersion relations for plate structures. For the discretization of the boundary, higher-order elements are employed to improve the efficiency of the simulations. The simplicity of mesh generation of a cracked plate for a scaled boundary finite element analysis is illustrated.

Physics of thermo-acoustic sound generation

We present a generalized analytical model of thermo-acoustic sound generation based on the analysis of thermally induced energy density fluctuations and their propagation into the adjacent matter. The model provides exact analytical prediction of the sound pressure generated in fluids and solids; consequently, it can be applied to arbitrary thermal power sources such as thermophones, plasma firings, laser beams, and chemical reactions. Unlike existing approaches, our description also includes acoustic near-field effects and sound-field attenuation. Analytical results are compared with measurements of sound pressures generated by thermo-acoustic transducers in air for frequencies up to 1 MHz. The tested transducers consist of titanium and indium tin oxide coatings on quartz glass and polycarbonate substrates. The model reveals that thermo-acoustic efficiency increases linearly with the supplied thermal power and quadratically with thermal excitation frequency. Comparison of the efficiency of our thermo-aco...

Ultrasonic field profile evaluation in acoustically inhomogeneous anisotropic materials using 2D ray tracing model: Numerical and experimental comparison.

Ultrasound propagation in inhomogeneous anisotropic materials is difficult to examine because of the directional dependency of elastic properties. Simulation tools play an important role in developing advanced reliable ultrasonic non destructive testing techniques for the inspection of anisotropic materials particularly austenitic cladded materials, austenitic welds and dissimilar welds. In this contribution we present an adapted 2D ray tracing model for evaluating ultrasonic wave fields quantitatively in inhomogeneous anisotropic materials. Inhomogeneity in the anisotropic material is represented by discretizing into several homogeneous layers. According to ray tracing model, ultrasonic ray paths are traced during its energy propagation through various discretized layers of the material and at each interface the problem of reflection and transmission is solved. The presented algorithm evaluates the transducer excited ultrasonic fields accurately by taking into account the directivity of the transducer, divergence of the ray bundle, density of rays and phase relations as well as transmission coefficients. The ray tracing model is able to calculate the ultrasonic wave fields generated by a point source as well as a finite dimension transducer. The ray tracing model results are validated quantitatively with the results obtained from 2D Elastodynamic Finite Integration Technique (EFIT) on several configurations generally occurring in the ultrasonic non destructive testing of anisotropic materials. Finally, the quantitative comparison of ray tracing model results with experiments on 32mm thick austenitic weld material and 62mm thick austenitic cladded material is discussed.

Numerical simulation of ultrasonic guided waves using the Scaled Boundary Finite Element Method

The formulation of the Scaled Boundary Finite Element Method is applied for the computation of dispersion properties of ultrasonic guided waves. The cross-section of the waveguide is discretized in the Finite Element sense, while the direction of propagation is described analytically. A standard eigenvalue problem is derived to compute the wave numbers of propagating modes. This paper focuses on cylindrical waveguides, where only a straight line has to be discretized. Higher-order elements are utilized for the discretization. As examples, dispersion curves are computed for a homogeneous pipe and a layered cylinder.

Influence of thermodynamic properties of a thermo-acoustic emitter on the efficiency of thermal airborne ultrasound generation

In this work we experimentally verify the theoretical prediction of the recently published Energy Density Fluctuation Model (EDF-model) of thermo-acoustic sound generation. Particularly, we investigate experimentally the influence of thermal inertia of an electrically conductive film on the efficiency of thermal airborne ultrasound generation predicted by the EDF-model. Unlike widely used theories, the EDF-model predicts that the thermal inertia of the electrically conductive film is a frequency-dependent parameter. Its influence grows non-linearly with the increase of excitation frequency and reduces the efficiency of the ultrasound generation. Thus, this parameter is the major limiting factor for the efficient thermal airborne ultrasound generation in the MHz-range. To verify this theoretical prediction experimentally, five thermo-acoustic emitter samples consisting of Indium-Tin-Oxide (ITO) coatings of different thicknesses (from 65 nm to 1.44 μm) on quartz glass substrates were tested for airborne ultrasound generation in a frequency range from 10 kHz to 800 kHz. For the measurement of thermally generated sound pressures a laser Doppler vibrometer combined with a 12 μm thin polyethylene foil was used as the sound pressure detector. All tested thermo-acoustic emitter samples showed a resonance-free frequency response in the entire tested frequency range. The thermal inertia of the heat producing film acts as a low-pass filter and reduces the generated sound pressure with the increasing excitation frequency and the ITO film thickness. The difference of generated sound pressure levels for samples with 65 nm and 1.44 μm thickness is in the order of about 6 dB at 50 kHz and of about 12 dB at 500 kHz. A comparison of sound pressure levels measured experimentally and those predicted by the EDF-model shows for all tested emitter samples a relative error of less than ±6%. Thus, experimental results confirm the prediction of the EDF-model and show that the model can be applied for design and optimization of thermo-acoustic airborne ultrasound emitters.

Resonanzfreie Messung und Anregung von Ultraschall

Zusammenfassung In diesem Beitrag präsentieren wir innovative Methoden für die breitbandige und resonanzfreie Messung und Anregung von Ultraschall. Das Messverfahren verwendet eine Kunststofffolie und ein Laser-Vibrometer als breitbandigen und resonanzfreien Empfänger. Im Allgemeinen ermöglicht dieses Verfahren eine präzise Messung der Schallschnelle und des Schalldruckes in beliebigen, für das Laserlicht transparenten Flüssigkeiten und Gasen mit bekannter Dichte und Schallgeschwindigkeit. Das resonanzfreie Senden von Ultraschall basiert auf einem elektro-thermo-akustischen Wandlerprinzip und ermöglicht, im Gegensatz zu herkömmlichen Ultraschallwandlern, die Erzeugung von beliebig geformten akustischen Signalen ohne Resonanzen und ohne Nachschwingen.

Approximate reconstruction of sound fields close to the source surface using spherical nearfield acoustical holography.

This paper presents an investigation of the reconstruction of sound field parameters close to the surface of arbitrarily shaped sound sources. The field is reconstructed using nearfield acoustical holography (NAH) in spherical coordinates. Of particular interest are source shapes where the Rayleigh hypothesis is violated. To overcome the limitation of the minimal sphere given by the validity restriction of the Rayleigh hypothesis an algorithm is proposed for extracting local information from the nonconvergent NAH solution. For the assessment of the results an appropriate virtual test rig is developed employing the Kirchhoff-Helmholtz integral theorem.

Thermoacoustic generation of airborne ultrasound using carbon materials at the micro- and nanoscale

The generation of airborne ultrasound is presented using the thermoacoustic principle applied to carbon materials at the micro- and nanoscale. Such materials are shown to be capable of emitting ultrasound when being fed by an alternating current. We tested the acoustic performance of carbon fibers, bucky papers and electrospun polyacrylonitrile-derived carbon nanofibers and determined the sound pressure for frequencies up to 350 kHz. A comparison between the experimental results and the theoretical prediction showed remarkable agreement for frequencies up to 150 kHz. Beyond 150 kHz, we found slight deviations from the expected sound pressure dependence on the square root of the frequency.

Computation of dispersion relations for axially symmetric guided waves in cylindrical structures by means of a spectral decomposition method.

In this paper, a method to determine the complex dispersion relations of axially symmetric guided waves in cylindrical structures is presented as an alternative to the currently established numerical procedures. The method is based on a spectral decomposition into eigenfunctions of the Laplace operator on the cross-section of the waveguide. This translates the calculation of real or complex wave numbers at a given frequency into solving an eigenvalue problem. Cylindrical rods and plates are treated as the asymptotic cases of cylindrical structures and used to generalize the method to the case of hollow cylinders. The presented method is superior to direct root-finding algorithms in the sense that no initial guess values are needed to determine the complex wave numbers and that neither starting at low frequencies nor subsequent mode tracking is required. The results obtained with this method are shown to be reasonably close to those calculated by other means and an estimate for the achievable accuracy is given.

Quantitative evaluation of ultrasonic sound fields in anisotropic austenitic welds using 2D ray tracing model

Ultrasonic investigation of inhomogeneous anisotropic materials such as austenitic welds is complicated because its columnar grain structure leads to curved energy paths, beam splitting and asymmetrical beam profiles. A ray tracing model has potential advantage in analyzing the ultrasonic sound field propagation and there with optimizing the inspection parameters. In this contribution we present a 2D ray tracing model to predict energy ray paths, ray amplitudes and travel times for the three wave modes quasi longitudinal, quasi shear vertical, and shear horizontal waves in austenitic weld materials. Inhomogenity in the austenitic weld material is represented by discretizing the inhomogeneous region into several homogeneous layers. At each interface between the layers the reflection and transmission problem is computed and yields energy direction, amplitude and energy coefficients. The ray amplitudes are computed accurately by taking into account directivity, divergence and density of rays, phase relations...