CALCULATION OF PARAMETERS OF ULTRASONIC WAVE IN ELASTIC MEDIA BY GALERKIN METHOD BASED ON WAVELET – FUNCTIONS
Keywords:
ultrasound, wavelet, galerkin's method, differential equation.Abstract
Development of numerical methods that calculates the parameters of ultrasonic wave's propagation in testing objects serves as source for both information for comparison with results of control and further analysis of the object state. It is presented the algorithm that calculates the method. The results of calculation are presented in a form of tables and charts. It is developed the method of calculation of differential equations that describe propagation of ultrasonic waves in solid media by Galerkin's approach that based on projection method with wavelets. In the result it is determined that with help of the developed method it is possible to perform analysis of parameters of ultrasonic wave propagation by Daubechies wavelets with level of 6, 8, and 10. Increasing level of Daubechies wavelets is requires increasing number of samplings for chosen way. This requires increasing the calculation time and computer resources while this approach do not increases substantially the precision. The method allows analysing propagation of wave with any lengths of ways. Increasing the lengths of path of propagation requires increasing the number of samplings of discretisation of differential equation. The results of calculation of differential equation can be compared with testing results it is allows to detect defects and changes of mechanical properties of media where propagating ultrasonic wave.
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