Oscillations and Waves in Viscoelastic Media with Inclusions - B.Sh. Usmonov; I.I. Safarov; B.Z. Nuriddinov (Oscillations and Waves in Viscoelastic Media with Inclusions, 2025)
Strong earthquakes that have occurred in recent years have shown that both underground and above-ground structures are destroyed by earthquakes. There are a large number of underground tunnels of various shapes located in seismically active areas that need to be protected from seismic impacts. Therefore, the development of methods for assessing the seismic impacts of underground structures and tunnels is an urgent problem at present. A significant amount of literature is devoted to determining the stress-strain state of underground structures using wave dynamics methods. The propagation of elastic waves in multiply connected regions (in the case of a plane problem, this is a plane or a half-plane with several cavities) is determined by the effects of diffraction on the cavities and interference of diffracted waves. The solution of these problems requires, first of all, the use of wave dynamics methods, since the interference effects that make the main contribution to the dynamic stress state of a multiply connected region cannot be taken into account in other ways. For the purposes of this paper, solutions to such problems are of considerable interest, since they reduce the problems of determining the seismic stress state of systems of closely located workings, which are often encountered in hydraulic engineering. These can be several parallel water conduit lines, a complex of rooms in a building, or an underground structure. The monograph is devoted to the analysis of problems on the dynamic stress state of multiply connected regions during the propagation of elastic waves. The paper considers the effect of harmonic waves on a cylindrical shell located in a viscoelastic half-plane. The main objective of the study is to determine the stress-strain state of a cylindrical shell under the influence of harmonic waves. The main equation of viscoelasticity in displacements with the corresponding boundary conditions is obtained. The problem is solved in the mixed potentials that satisfy the wave equation with complex parameters. The solution is expressed through the special Bessel and Hankel functions. As a result of multiple reflection, a system of algebraic equations with complex coefficients is obtained. In the future, this system is solved by the Gauss method with the allocation of the main element. The analytical solution is obtained in infinite series, the convergence of which is studied numerically. Numerical results are obtained on the MATLAB software package. The reliability of the obtained research results is confirmed by good agreement with theoretical and experimental results and those obtained by other authors. The monograph consists of eleven chapters. The first chapter provides a review of the literature. The remaining chapters solve the problems of diffraction and interaction of waves with bodies of various shapes.