Nonstationary Deformation of Cylindrical shells Under a Plane Pressure Wave

Abstract

Nonstationary deformation of a cylindrical shell located in an infinite elastic medium is studied under plane pressure wave with a front parallel to the shell axis. A combined solution method is used in the paper. Separating the angular coordinate by the Fourier method, the plane problem is reduced to a series of one-dimensional problems for each harmonic. Applying the Laplace transform over time to these systems of equations, the exact solution in the images is obtained. Asymptotic solutions of the stress-strain state at large values of time t → ∞ are obtained. In parallel with this, a truncated system is numerically solved using an explicit finite-difference scheme and a method for minimizing numerical dispersion, which gives an accurate description of front discontinuities. A comparison of both solutions made it possible to determine the applicability limits of the asymptotic forms and to obtain an assessment of dynamic state of shell and medium during the entire time of interaction.

Longitudinal vibrations of underground pipelines of finite length in medium surrounded by soil with different properties along pipeline length

“…In [7][8][9][10][11][12][13][14][15][16], various mechanical and mathematical models were analyzed, and several topical problems of underground and surface structures were solved.…”