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Название: Nicht axialsymmetrische Wellenausbreitung in anisotropen zylindrischen Strukturen
Автор: Gsell D.
In this thesis, guided wave propagation in cylindrical, anisotropic structures is studied in a frequency range up to 1 MHz. The investigations are carried out with carbon fibre reinforced tubes. The emphasis is the experimental determination of their effective linear elastic material properties. The wavelengths of axially propagating waves, guided by the two lateral surfaces of the tube, are influenced considerably by the elastic material parameters. In the context of this work, this relation is used in order to determine the different material properties experimentally, by solving the inverse problem.
In the experiments the surface displacements of travelling waves are measured along the axis of the tube with a laser interferometer. The elastic waves are generated by piezoelectric elements. The extraction of the dispersion curves is achieved by two dimensional spectrum analysis. The procedure is based on a Fourier transformation
in time and on a Matrix-Pencil algorithm in space domain in order to decompose the wave numbers. It was developed in the areas of Nuclear Magnetic Resonance.
Two different material models are examined: a general, cylindrically orthotropic model based on nine independent constants, and a laminated model, whereby the individual layers are assumed as transversely isotropic with different orientation with respect to the axis of the tube.
A sensitivity investigation shows that in the first model only four stiffness elements have a substantial influence on the dispersive behavior of the waves, while in the second case only three of them are involved. For the theoretical description of the dispersion relation we avail ourselves of a numerical-analytical procedure, which is based on Hamilton’s principle. In time, tangential, and axial direction, global trigonometric functions are used, while the problem is discretized in radial direction and the solution is approximated by finite elements. Linear displacement functions are incorporated in these elements.
The solution of the inverse problem is done by the method of total least squares. The squares of the errors in the observation space, weighted with the cofactor matrices, are minimized. To obtain a robust optimization algorithm with respect to outliers in the input data, the residues are used to classify the data points into inand outliers. Therefore outliers can be excluded from the input data.
In order to test and validate the presented method systematically, artificially generated data are used. Therefore, the wave propagation in the tube, as well as the piezoelectric excitation are simulated with the finite-difference method in time domain. The validation of the algorithm is based on the observation of the total mechanical energy as well as the determination of dispersion curves and their comparison with the theoretically determined relation. High accuracy in the extracted linear elastic material properties, obtained by analyzing such artificially generated data, confirms the suggested methodology. As a by-product the developed tool can be used for the visualization of the wave propagation in anisotropic tubes and contributes to the understanding of these complex phenomena.
To verify the simulation algorithms as well as for the determination of elastic material parameters non axisymmetric wave experiments are performed. The mechanical disturbances are excited piezoelectrically and are detected by a laser interferometer. The comparisons of time signals between the physical and the numerical experiments, validates the capability of the simulation algorithm to describe the physics appropriately. This can also be shown by comparing transfer functions instead. The determinable elastic properties of the analyzed carbon fibre reinforced tubes can be extracted successfully in the used frequency range.