This article analyzes the transient wave propagation phenomena that take place at 2D viscoelastic half-spaces subjected to spatially distributed surface loadings and to distinct temporal excitations. It starts with a fairly detailed review of the existing strategies to describe transient analysis for elastic and viscoelastic continua by means of the Boundary Element Method (BEM). The review explores the possibilities and limitations of the existing transient BEM procedures to describe dynamic analysis of unbounded viscoelastic domains. It proceeds to explain the strategy used by the authors of this article to synthesize numerically fundamental solutions or auxiliary states that allow an accurate analysis of transient wave propagation phenomena at the surface of viscoelastic half-spaces. In particular, segments with spatially constant and linear stress distributions over a halfspace surface are considered. The solution for the superposition of constant and discontinuous adjacent elements as well as linear and continuous stress distributions is addressed. The influence of the temporal excitation type and duration on the transient response is investigated. The present study is based on the numerical solution of stress boundary value problems of (visco)elastodynamics. In a first stage, the solution is obtained in the frequency domain. A numerical integration strategy allows the stationary solutions to be determined for very high frequencies. The transient solutions are obtained, in a second stage, by applying the Fast Fourier Transform (FFT) algorithm to the previously synthesized frequency domain solutions. Viscoelastic effects are taken into account by means of the elastic-viscoelastic correspondence principle. By analyzing the transient solution of the stress boundary value problems, it is possible to show that from every surface stress discontinuity three wave fronts are generated. (continued on next The displacement velocity of these wave fronts can be associated to compression, shear and Rayleigh waves. It is shown that the half-space transient displacement solutions present abrupt jumps or oscillations which can be correlated to the arrival of these wave fronts at the observation point. Such a detailed analysis connecting half-space transient responses to the wave propagation fronts in viscoelastic half-spaces have not been reported in the reviewed literature.

SUMMARYIn this article a numerical solution for a three-dimensional isotropic, viscoelastic half-space subjected to concentrated surface stress loadings is synthesized with the aid of the Radon and Fourier integral transforms. Dynamic displacement and stress fields are computed for points at the surface and inside the domain. The analysis is performed in the frequency domain. Viscoelastic effects are incorporated by means of the elastic-viscoelastic correspondence principle. The equations of motion are solved in the Radon-Fourier transformed domain. Inverse transformations to the physical domain are accomplished numerically. The scheme used to perform the numerical inverse transformations is addressed. The solution is validated by comparison with results available in the literature. A set of original dynamic displacement and stress solutions for points within the half-space is presented.

SUMMARYIn this article a numerical solution for a 3D isotropic, viscoelastic half-space subjected to vertical rectangular surface stress loading of constant amplitude is evaluated with the aid of the Radon and Fourier integral transforms. Dynamic displacement and stress fields are computed for the half-space surface as well as for points inside the domain. The analysis is performed in the frequency domain. Viscoelastic effects are incorporated by means of the elastic-viscoelastic correspondence principle. The equations of motion are solved in the Radon-Fourier transformed domain. Inverse transformations to the physical domain are accomplished numerically. The scheme used to perform the numerical inverse transformations is addressed. The solution is validated by comparison with results available in the literature. A sample of original dynamic results for displacement and stress fields for the 3D half-space is furnished.

No abstract