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.
The task of determining the dynamic response of plates and shells to moving loads is very relevant. The purpose of this work is to study the stationary deformation of infinitely long cylindrical shells with viscoelastic filler when moving along the axis of the shell of a wave of normal pressure with up to resonant velocity under the influence of normal moving loads. The paper presents a mathematical formulation of the problem, developed methods of solution and obtained numerical results. The solution methods are based on the joint application of the integral Fourier transform in the axial coordinate and the decomposition of all given and desired values into Fourier series in the angular coordinate. An effective algorithm for solving the problem has been developed and implemented on a computer. It is established that with the distance from the point of application of force along the circumference of the voltage for all considered cases, the sign changes. If the connection is one-sided, then tensile stresses arise, and the shell will detach from the filler. It has also been found that changes in the stiffness and rheological properties of the filler in the considered range have little effect on the length of the contact zone.
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