Hyperbolic boundary layers in compound cylindrical shells

Abstract

A survey of papers dealing with the mathematical modeling of transient wave propagation in compound and stiffened shell constructions by asymptotic methods based on exact three-dimensional elasticity equations can be found in [1]. Longitudinal actions of tangential and bending types are considered. An asymptotic model of wave propagation in a semi-infinite shell of rotation is used, which employs the two-dimensional Kirchhoff-Love (tangential and flexural) components, the solutions of the quasiplane problem of elasticity, the parabolic boundary layer near the quasifront, and the hyperbolic boundary layer near the expansion wave front. The boundary value contact problems for the incident, reflected, and transmitted waves are posed and solved on the basis of approximate theories for the corresponding components. If the boundary conditions are satisfied at the shell faces in the exact three-dimensional form in small neighborhoods of the shell end contact region, then the construction of the quasistatic boundary layer satisfying the boundary conditions together with the two-dimensional component is completed. Methods proposed for solving boundary value problems by using integral transforms and asymptotic approaches to their inversion are described. But the methods developed for constructing hyperbolic boundary layers near the wave fronts are not described in [1].