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- Dispersion (5)
- Guided waves (5)
- Lamb waves (5)
- Scaled boundary finite element method (5)
- Ray tracing (4)
- Non-destructive testing (3)
- SAFT (3)
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- Ultrasound (3)
- Airborne ultrasound transducer (2)
Organisationseinheit der BAM
In this paper, a method is presented for the numerical computation of dispersion properties and mode shapes of guided waves in plate structures. The formulation is based on the Scaled Boundary Finite Element Method. The through-thickness direction of the plate is discretized in the finite element sense, while the direction of propagation is described analytically. This leads to a standard eigenvalue problem for the calculation of wave numbers. The proposed method is not limited to homogeneous plates. Multi-layered composites as well as structures with continuously varying material parameters in the direction of thickness can be modeled without essential changes in the formulation. Higher-order elements have been employed for the finite element discretization, leading to excellent convergence for complex structures. It is shown by numerical examples that this method provides highly accurate results with a small number of nodes while avoiding numerical problems and instabilities.
This paper presents the numerical modeling of the Lamb wave propagation in thin plates with the elastodynamic finite integration technique (EFIT) and its validation with the measured results. In general, Lamb waves offer an attractive method to detect the defects inside long plate like structures efficiently. However, such a nondestructive testing (NDT) requires profound understanding of the Lamb wave propagation in the plates, generation of the symmetric and anti-symmetric modes of different orders and their interaction with the defects of the materials. Modern simulation tools based on numerical methods such as the finite integration technique (FIT), the finite element method (FEM) and the boundary element method (BEM) can be used to model this NDT situation. The elastodynamic finite integration technique (EFIT) is an effective tool to model Lamb wave propagation in plates over long distances in an efficient way. With the help of the simulation results obtained from the EFIT tool the propagation of different symmetric and anti-symmetric modes is analyzed and thus a proper technique is developed to excite different modes and to separate them from each other precisely. A validation of the numerical results with the analytical results is also presented.
In this paper the Scaled Boundary Finite Element Method (SBFEM) is applied for the simulation of Lamb waves in cracked plates. This method is highly advantageous to study the interaction of different Lamb wave modes with cracks as the crack is not discretized and no refinement is required around the crack tip. Numerical examples are presented for the reflection of the fundamental symmetric and antisymmetric modes from cracks of different depth. The spatial Fourier transformation is employed to calculate the amplitudes of reflected Lamb wave modes. The results reveal possibilities to obtain details of the crack geometry in non-destructive testing and structural health monitoring applications.
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 as well as transmission coefficients. Ultrasonic sound fields obtained from the ray tracing model are compared quantitatively with the 2D Elastodynamic Finite Integration Technique (EFIT). The excellent agreement between both models confirms the validity of the presented ray tracing results. Experiments are conducted on austenitic weld samples with longitudinal beam transducer as transmitting probe and amplitudes at the rear surface are scanned by means of electrodynamical probes. Finally, the ray tracing model results are also validated through the experiments.
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 testing techniques for the inspection of anisotropic materials particularly austenitic cladded materials and dissimilar welds. A 2-D Ray tracing method is developed for evaluating ray path, amplitude and travel time for three wave modes namely quasi longitudinal wave (qP), quasi shear vertical wave (qSV) and shear horizontal waves (SH) in anisotropic materials such as austenitic cladded materials. The inhomogenity in the anisotropic material is represented by discretizing the anisotropic region into several homogeneous layers. The ray paths are traced during its propagation through the various interfaces between those layers. At each interface the problem of reflection and refraction is solved. The ray amplitudes are computed by taking into account the directivity and phase relations. Ray divergence variation and ray transmission coefficients at each refraction boundary are considered. The Ray tracing results for ultrasonic field profiles in austenitic cladded materials are validated quantitatively by 2-D Elastodynamic Finite Integration Technique (EFIT) results and by the experiments.
The Synthetic Aperture Focusing Technique (SAFT) is an algorithm applied in non-destructive ultrasonic testing which provides an image of flaws within a specimen. The image is reconstructed from A-scans measured at different positions. Reliable evaluation of the images obtained by the SAFT-algorithm, however, depends on the representation of the reconstructed data, which is initially given in terms of positive and negative local values only. A suitable way of processing this data for evaluation is to calculate the envelope, which can be achieved by means of the analytic signal. The extension of this concept to the multidimensional case is neither trivial nor unique and although extensive work on this subject has been carried out in the past, a correct envelope calculation in multidimensional data remains difficult since it depends on an additional condition, namely the separability of the signal. In this paper, the concept of analytic signals with single-quadrant spectra is applied to process 2-dimensional data obtained by the SAFT-algorithm. Furthermore, we present a procedure to overcome the limitations of that approach by selecting local magnitude values from a number of rotated frames after evaluating the signals separability in each frame, which is briefly validated against synthetic and experimental data.
In this paper, a numerical approach for the computation of dispersion relations for three-dimensional waveguides with arbitrary cross-section is proposed. The formulation is based on the Scaled Boundary Finite Element Method (SBFEM). It is an extension of the approach previously derived for plate structures. It is shown that the wavenumbers of guided waves in a waveguide can be obtained as the eigenvalues of the Z matrix, which is well known in the SBFEM. The Hamiltonian properties of this matrix are utilized to derive an efficient way to compute the group velocities of propagating waves as eigenvalue derivatives. The cross-section of the waveguide is discretized using higher-order spectral elements. It is discussed in detail how symmetry axes can be utilized to reduce computational costs. In order to sort the solutions at different frequencies, a mode-tracking algorithm is proposed, based on the Padé expansion.
Lamb waves travel in plates and hollow cylinders over large distances and propagate with multiple mode shapes. Therefore the waves can be used for integrity tests of large scale structures. Each propagating wave mode has a unique dispersive character and a frequency dependent vibration pattern. Therefore, by interacting with flaws each mode is assumed to generate an individual reflection pattern depending on the flaw type, flaw orientation and size. To extract this information a frequency as well as wave number dependent mode excitation is required ensuring a single mode excitation. The challenge, however, is to control the selective mode excitation electronically to allow a sequence of consecutive tests with different wave modes to collect the data. A method is proposed using phased array wedge transducers with fluid coupling for normal force excitation of Lamb wave modes. The excitation principle is investigated analytically on plates by modelling the wave generation in the wedge and the coupling between wedge and structure. The analytical results of the excitation principle are validated by corresponding experiments where the field patterns on the wedge surface and on the plate were scanned using a laser vibrometer. The directivity of the radiated field is investigated together with the direction dependent analysis of the mode content.
In this study a method for early damage detection is investigated based on the directed excitation and measuring of Lamb waves (guided waves). The objective is to make a statement about the practicability of a Lamb wave generator (LWG) and about the application relevant parameters (specimen materials and dimensions, wave characteristics, excitation, transmission und reflection). Guided waves enable an effective differentiation of structural and defective indications as well as a classification of different defect types. For the investigations, a LWG was developed which combines the advantages of the single excitation of a piezoelectric actuator and the possibility of a group excitation. Algorithms were developed to identify and analyze damage patterns (cracks, wholes, weakening).
Up to now there is no sufficient technique to detect transverse cracks in austenitic and dissimilar welds which recently are of increasing interest in the integrity surveillance of nuclear power plants as well as in quality control of longitudinally welded pipes. Weld inspection by interpretation of single A-scans will lead to erroneous results due to effects caused by anisotropy and in worst case might leave flaws undetected. Therefore, imaging techniques such as the synthetic aperture focusing technique (SAFT) should be used. If the SAFT algorithm is applied on data taken from austenitic welds, the inhomogeneous, anisotropic structure of these welds has to be taken into account in order to properly attribute amplitudes measured in A-scans to the corresponding coordinates in the region of interest. While this has been investigated in the past, all attempts so far were limited to the imaging of longitudinal cracks which requires a less complicated setup than the imaging of transverse cracks. In this paper we give an outline of our attempts to reconstruct images of transverse cracks in different welds. For this purpose a SAFT program based on ray tracing and a layered structure weld model derived from an empirical model of grain orientations in welds are used. The results of the image reconstruction on experimental data are shown and compared to images obtained by assuming an isotropic homogeneous model. Root reflection and crack tip echo are clearly visible which allows an estimation of size and position of the crack with good accuracy.