Numerical modeling of dispersion phenomena in thick plate
This paper reports on a technique for the analysis of propagating multimode signals. The method involves a 2-D Fourier transformation of the time history of the waves received at a series of equally spaced positions along the propagation path. The output of the transform being presented using an isometric projection that gives a 3-D view of the wave number dispersion curves. The time history of the waves was obtained by the commercial finite element (FE) code, MARC. The results of numerical studies and the dispersion curves of Lamb waves propagating in the 2.0-mm-thick steel plate are presented. The results are in good agreement with analytical predictions and show the effectiveness of using the 2-D Fourier transform method to identify and measure the amplitudes of individual Lamb modes.
The elastic wave propagation in prismatic bodies with the sharp shape transitions
Due to using non-destructive diagnostics method - the acoustic emission- the best knowledge of the rules of the elastic wave propagation in bodies are required. So this work treats the elastic wave propagation in the basic elements of structures. The samples with the most common shape transitions are used - here experimental bodies with the offsets (like a stair shape) at various sizes. The results of the analytical computations (generalized ray theory), numerical simulations (the finite element method implemented in software MARC/MENTAT) and experimental results (broadband piezoceramics transducers) are verified and compared mutually.
Dispersion mode separation in ultrasonic signal processing
This paper reports on a technique for the analysis of propagating multimode signals. The method involves a 2-D Fourier transformation of the time history of the waves received at a series of equally spaced positions along the propagation path. The output of the transform being presented using an isometric projection that gives a 3-D view of the wave number dispersion curves. The time history of the waves was obtained by the commercial finite element (FE) code, MARC. The results of numerical studies and the dispersion curves of Lamb waves propagating in the 2.0-mm-thick steel plate are presented. The results are in good agreement with analytical predictions and show the effectiveness of using the 2-D Fourier transform method to identify and measure the amplitudes of individual Lamb modes.
The elastic wave propagation over the shape transitions of bodies
Due to using non-destructive diagnostics method - the acoustic emission- there is required the best knowledge about the rules of the elastic wave propagation in bodies. So this work treats the elastic wave propagation in the basic construction elements of structures. The samples with the most common shape transitions are used - here some experimental bodies with the shoulders (like a stair shape) at various sizes. The results of the analytical computations, numerical simulations and experimental results are verified and compared mutually. The generalized ray theory - one from the analytical methods - is applied. For the extensive numerical simulations the finite element method (implemented in software MARC/MENTAT) is used. The transient piezoceramics transducers are employed for the experimental measuring.
Numerical modeling and experimental evaluation of geometrical dispersion effects
For precise acoustic emission (AE) source localization and quantitative AE signal processing it is necessary to analyze signal distortion caused by wave propagation from the source to receiving sensor. Dominant wave modes propagating in thin-walled structures are so called guided waves which exhibit strong dispersion. Experimental determination of the structural impulse response, based on a point source/receiver technique, is necessary to evaluate signal distortion in such structures.
Analysis of Dispersive Stress Waves by means of Continuous Wavelet Transform
The time-frequency analysis of dispersive stress waves is reviewed. It is shown that the wavelet transform using the Morlet pseudowavelet effectively decomposes the strain response into its time-frequency components and that the wavelet transform enables us to identify the dispersion relation of the group velocity.
Using of the Continuous Wavelet Transform to the Time-frequency Analysis of the Dispersive Stress Waves
The time-frequency analysis of dispersive stress waves is reviewed. It is shown that the wavelet transform using the Morlet pseudowavelet effectively decomposes the strain response into its time-frequency components and that the wavelet transform enables us to identify the dispersion relation of the group velocity.
Wavelet Packet Analysis
The wavelet packet method is a generalization of wavelet decomposition that offers a richer signal analysis. Wavelet packet atoms are waveforms indexed by three naturally interpreted parameters: position and scale (as in wavelet decomposition) and frequency. For a given orthogonal wavelet function, we generate a library of wavelet packet bases. Each of these bases offers a particular way of coding signals, preserving global energy and reconstructing exact features. The wavelet packets can then be used for numerous expansions of a given signal. We then select the most suitable decomposition of a given signal with respect to an entropy-based criterion.
Multiplication of matrices using the wavelet approach
In this paper is described the algorithm for the rapid numerical applying a dense matrix N x N to a vector. As is well known, applying directly a dense N x N - matrix to a vector requires roughly N^2 operations, and this simple fact is a cause of serious difficulties encountered in large-scale computations. The algorithm of this paper require order O(N logN) operations.
