br Convergence study and computational results To

Convergence study and computational results To adequately choose the size of the finite elements and the integration step, we examined the convergence of the results as a function of these parameters. Given the physical nature of the simulated vibration process, the grid dimension and the integration step will depend on the longitudinal wavelength λ in the material and the period of oscillation T = 1/f. Studying the convergence results versus the dimension of the FE model involved a series of computations with the integration time step taken to equal 0.1T. The characteristic size of the element\'s side varied in the range from 5 to 33% of the elastic longitudinal wavelength λ. The analysis of the obtained solutions revealed that they are weakly dependent on the size of the p2y receptor and that a further decrease in the element size has virtually no effect on the results for an element side less than 25% of the wavelength. The dependence of the computational results as a function of the integration step was examined with the integration step varied within the range between 1 and 15% of the oscillation period. The signal generated by the piezoelectric element receiving the reflected wave is shown in Fig. 4 at different values of the integration step. It can be seen that the solution is highly sensitive to the step value. The qualitative agreement between the results can only be achieved with an integration step less than 5% of the oscillation period. At the same time, the shape of the signal envelope obtained in the simulation with small time steps is significantly different from the one observed in the experiment. A ‘narrowing’ of the wave package occurs, which should inevitably lead to distortions in the magnitude of acoustic anisotropy (Fig. 5). For more detailed analysis of the obtained results, we plotted the dependence of the time delay in the rising edge of an average package pulse (according to the operating principles of the measuring instrument) versus the integration time step (Fig. 6). Convergence is not discernible in the graph. Reducing the step leads to an almost linear decrease in the delay time. Thus, to obtain a good agreement with the experimental data, it is necessary to keep track of the integration step and take into account the emerging delay, specifically adding it to the results of the simulation ‘measurements’.
Conclusion
Acknowledgment This study was financially supported by a grant of the Russian Science Foundation (project no. 15-19-00091).