Model of wave propagation in single-layer homogenous anisotropic media
The purpose of this study is to verify the numerical simulation of the finite difference method of the wave propagation in single-layer homogenous anisotropic media and materials with variations in the anisotropy parameters. In this way, the effects of a type of anisotropy, specifically transverse isotropy (system with elastic hexagonal or polar symmetry) can be evaluated in the propagation of waves in elastic media by ultrasonic inspection. The algorithm for the construction of the model applies the finite difference method and was created in FORTRAN language. The evaluated approach is in two-dimensional space. In the simulations with the single-layer homogenous anisotropic model, snapshots of the displacement components were generated in the x and z directions, on which observations were made regarding the effects of the anisotropy parameters on wavefront behavior. The results are in attachment for wide dissemination. This model aims to expose the behavior of wave fronts in relation to variations in anisotropy parameters. The models are formed by a half-plane xz with 2500 x 2500 points. The time frame adopted for this case was 6.5s for each situations. This led to 15 different parameter variations (see data in attachment). The elements present the snapshots of these situations in the single-layer homogenous anisotropic model with horizontal and vertical components of the displacement field, where the source is located at the center of the model. With the images of the displacement field, it is possible to evaluate the profile of the propagated P and S wave fronts for each situation.
Steps to reproduce
With all properties entered in the model, the propagation process is ready to start. The simulation of wave propagation begins with an impulsive energy source represented by an analytical function. This source was inserted on the center of the model. The source used for the numerical simulation is an explosive type and 500Hz frequency, located on the center of the model. The process of wave propagation occurs initially through a perturbation in initial condition through an analytical excitation defined by the second-order derivative of the Gaussian function. With the explosion of the source, propagation begins. As the finite difference method is based on the elastic wave equation and not on particular solutions, it includes both direct waves (P and S) as well as surface waves, refracted, diffracted and converted; and still preserves the amplitude relations of events. The data in attachments exposes the simulated results by: (i) the images of the displacement field components in 6.5s, (ii) components of the x-direction field of displacement, (iii) components of the z-direction field of displacement, and (iv) slowness profile with variant anisotropic parameter. With the images of the displacement field components, it is possible not only to obtain the format of the propagated P and S wave fronts but also the slowness profile with variant anisotropic parameter. Homogeneous models have the following characteristics in common: • Sampling mesh of 2500 x 2500 points, square, with spatial sampling interval adjusted to 1.1x10-5 mm; • Density of 5900 kg / m2; • Cutting frequency set at 500 Hz; • Time sampling interval of 3.2 x10-9s to 5x10-9s for a total of 6.5 s, • Process of propagation initiated through a source positioned in the center of the model. The images of the components of the displacement field of the results in attachments are examples of the results in the propagation time of 6.5s, where the phenomenon can be verified, providing a better visualization of the evolution of the process of propagation of the ultrasonic waves in single-layer homogenous anisotropic media.