Transient wave processes in viscoelastic structures built from functionally graded material (FGM) still remain almost unexplored. In this article, the problem of the propagation of nonstationary longitudinal waves in an infinite viscoelastic layer of a FGM with plane–parallel boundaries is considered. The physical and mechanical parameters of the FGM depend continuously on the transverse coordinate, while the wave process propagates along the same coordinate. The viscoelastic properties of the material are taken into account employing the linear integral Boltzmann–Volterra relations. The viscoelastic layer of the FGM is replaced by a piecewise-homogeneous layer consisting of a large number of sub-layers (a package of homogeneous layers), thus approximating the continuous inhomogeneity of the FGM. A solution of a non-stationary dynamic problem for a piecewise-homogeneous layer is constructed and, using a specific example, the convergence of the results with an increase in the number of sub-layers in the approximating piecewise-homogeneous layer is shown. Furthermore, the problem of the propagation of nonstationary longitudinal waves in the cross section of an infinitely long viscoelastic hollow FGM cylinder, whose material properties continuously change along the radius, is also considered. The cylinder composed of the FGM is replaced by a piecewise-homogeneous one, consisting of a large number of coaxial layers, for which the solution of the non-stationary dynamic problem is constructed. For both the layer and the cylinder composed of a viscoelastic FGM, the results of calculating the characteristic parameters of the wave processes for the various initial data are presented. The influence of the viscosity and inhomogeneity of the material on the dynamic processes is demonstrated.

A problem of non-stationary longitudinal wave propagation in the cross-section of an infinite hollow linear-viscoelastic cylinder with coaxial elastic inclusion is considered. On the contact surfaces between the layers, continuity of displacements and stresses is assumed. The solution of the problem is constructed using the integral Laplace transform in time with subsequent reversal. For the case when each of the relaxation kernels is a finite sum of exponentials, the original is presented as a series of residues. Thus, the process of constructing a non-stationary solution is reduced to the search for the roots of the characteristic transcendental equation. The derived solution allowed to investigate the transient wave propagation in a viscoelastic cylinder with coaxial elastic inclusion with specified initial data.

On 22 May 2012, a magnitude Mw 5.6 earthquake struck the Pernik region of western Bulgaria, causing structural damage in nearby cities, including Sofia. This study assesses the seismic response of a six-story reinforced concrete building in central Sofia, utilizing real accelerogram data recorded at the basement (SGL1) and sixth floor (SGL2) levels during the earthquake. Using the Kanai–Yoshizawa (KY) model, the study estimates inter-story motion and assesses amplification effects across the structure. Analysis of peak ground acceleration (PGA), velocity (PGV), displacement (PGD), and spectral ratios reveals significant dynamic amplification of peak ground acceleration and displacement on the sixth floor, indicating flexible and dynamic behavior, as well as potential resonance effects. The analysis combines three spectral techniques—Horizontal-to-Vertical Spectral Ratio (H/V), Floor Spectral Ratio (FSR), and the Random Decrement Method (RDM)—to determine the building’s dynamic characteristics, including natural frequency and damping ratio. The results indicate a dominant vibration frequency of approximately 2.2 Hz and damping ratios ranging from 3.6% to 6.5%, which is consistent with the typical damping ratios of mid-rise concrete buildings. The findings underscore the significance of soil–structure interaction (SSI), particularly in sedimentary basins like the Sofia Graben, where localized geological effects influence seismic amplification. By integrating accelerometric data with advanced spectral techniques, this research can enhance ongoing site-specific monitoring and seismic design practices, contributing to the refinement of earthquake engineering methodologies for mitigating seismic risk in earthquake-prone urban areas.