Dynamic Stress-Deformed States of a Circular Tunnel of Small Position Under Harmonic Disturbances

¹ Institute of Mechanics and Seismic Resistance of Structures of the AS R Uz, Tashkent
² Mathematics Department, Bukhara engineering-technological institute, Bukhara, Uzbekistan
³ Bukhara medical institute, Bukhara, Uzbekistan
⁴ Tashkent Institute of Chemical Technology, Tashkent, Republic of Uzbekistan
⁵ Mathematics and Natural Sciences Department, Bukhara branch of the Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, Bukhara, Uzbekistan

^* Corresponding author: boltayev-z@mail.ru

Abstract

There are many underground tunnels of various shapes located in seismically active areas that need to be protected from seismic impacts. The paper considers the impact of harmonic waves on a cylindrical shell located in a viscoelastic half-plane. The study's main purpose is to determine the stress-strain state of a cylindrical shell when exposed to harmonic waves. The basic equation of viscoelasticity in displacements with the corresponding boundary conditions is obtained. The problem posed is solved in mixed potentials that satisfy the wave equation with complex parameters. The solution is expressed in terms of special Bessel and Hankel functions. As a result of multiple reflections, a system of algebraic equations with complex coefficients is obtained. In the future, this system is solved by the Gauss method with the selection of the main element. The analytical solution is obtained in infinite series, the convergence of which is investigated numerically. The numerical results were obtained using the MATLAB software package. The reliability of the research results is confirmed by good agreement with theoretical and experimental results and those obtained by other authors.