Dynamic behavior of material strength due to the effect of prestress, aeolotropy, non-homogeneity, irregularity, and porosity on the propagation of torsional waves

Abstract

This paper investigates the dynamic behavior of material strength due to the traction and propagation of torsional surface waves. Dynamic behavior of material strength depends on non-homogeneity, aeolotropy, irregularity, porosity, and internal prestress in an elastic body. The geometry of the model is constructed by a local-elastic, highly non-homogeneous finite thickness layer over a trigonometric variation of non-homogeneous aeolotropic porous half-space. The surface boundaries of both the free surface and interface are considered corrugated boundaries. The separation variable technique is used to solve the equation of motions (hyperbolic type PDEs), and the Bessel function is adopted in the displacement components of torsional waves for both the media. Because of highly non-homogeneity in the upper layer, the equation of motion comprises a special form of differential equation called Whittaker differential equation, and the solution (as displacement) of the equation is obtained in the form of Whittaker functions. The quantitative prediction of a differential equation is one of the significant tasks in the study of wave propagation, thus, the dispersion equation of the torsional surface waves is introduced analytically with the help of traction-free and continuity conditions. The validity of the final dispersion equation is described using several particular cases. To study the intensity of the torsional surface waves in the model, traction components have been computed along the coordinate axes, which helps to detect the material fracture in the medium. MATLAB software is used to study the dynamic behavior of the phase velocity, under the influence of prestressing irregular boundary surface, non-homogeneity, and porosity parameters in the media. By the numerical simulations, some marvelous changes in the propagation of the torsional surface waves due to the irregularity at the interface and free surface are obtained. The work may be useful to study the behavior of torsional surface waves in the micro-structure material and smart material composite structures used in the aerospace industry and seismology. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature.