Dynamic Stresses near a Supported Cylindrical Rupture Surface During under Harmonic Wave

An infinitely long circular cylinder generally consisting of an arbitrary number of coaxial viscoelastic layers surrounded by a viscoelastic medium is considered. It is assumed that the layered package consists of thick-walled and thin-walled layers of the cylinder. When describing the motion of thin-walled elements, the equations of the theory of such shells are used, which are based on the Kirchhoff–Love hypotheses. For thin-walled layers, the initial equations are based on the linear theory of elasticity. The problem is solved by the Green–Lamb method. The displacement potentials are determined from the solutions to the Helmholtz equation. Arbitrary constants are determined from the boundary conditions that are set between the bodies. As a result, the problem is reduced to a system of inhomogeneous algebraic equations with complex coefficients, which is solved by the Gaussian elimination method with pivoting. Analytical expressions for dynamic displacements and stresses in layers and the environment are obtained in terms of special Bessel and Hankel functions. It was found that, for $${{R}_{1}}{\text{/}}{{r}_{0}} > 50$$ , the effect of a cylindrical source is decomposed as a plane wave; i.e., the curvature radius of the wave may be ignored.

Hali tarjima qilinmagan