Approximate fundamental solutions and wave fronts for general anisotropic materials

AbstractThe time-dependent differential equations of elastodynamics for homogeneous solids with a general structure of anisotropy are considered in the paper. A new method of computation of the fundamental solution for these equations is proposed. This method consists of the following. Applying the Fourier transformation with respect to space variables to these equations, we obtain a system of second order ordinary differential equations whose coefficients depend on Fourier parameters. Using the matrix transformations and properties of the coefficients, the Fourier image of the fundamental solution is computed. Finally, the fundamental solution is calculated by the inverse Fourier transformation to the obtained Fourier transform. The implementation and justification of the suggested method have been made by computational experiments in MATLAB. These experiments confirm the robustness of the suggested method. The visualization of the displacement components in general homogeneous anisotropic solids by modern computer tools allows us to see and evaluate the dependence between the structure of solids and the behavior of the displacement field. Our method allows users to observe the elastic wave propagation, arising from pulse point forces of the form emδ(x)δ(t), in monoclinic, triclinic and other anisotropic solids. The visualization of displacement components gives knowledge about the form of fronts of elastic wave propagation in Sodium Thiosulfate with monoclinic and Copper Sulphate Pentahydrate with triclinic structures of anisotropy