Analysis of phase diagram of beryllium at high pressures and temperatures obtained as a result of ab initio calculations and large scale classical molecular dynamics simulations of beryllium shock loading have shown that the so called cold melting takes place when shock wave propagates through polycrystalline samples. Comparison of ab initio calculation results on sound speed along the Hugoniot with experimental data obtained on Z-machine also evidences for possible manifestation of the cold melting. The last may explain the discrepancy between atomistic simulations and experimental data on the onset of the melting on the Hugoniot.
The paper studies the interaction of a spherical shock wave with an elastic circular cylindrical shell immersed in an infinite acoustic medium. The shell is assumed infinitely long. The wave source is quite close to the shell, causing deformation of just a small portion of the shell, which makes it possible to represent the solution by a double Fourier series. The method allows the exact determination of the hydrodynamic forces acting on the shell and analysis of its stress state. Some characteristic features of the stress state are described for different distances to the wave source. Formulas are proposed for establishing the safety conditions of the shell.Consider an infinitely long elastic circular cylindrical shell immersed in an infinite fluid. A point source of shock waves (SWs) is located at a distance R 0 from the shell axis. A spherical SW is diffracted by the shell, and while deforming, the shell generates radiation waves. Therefore, the stress analysis of the shell must involve the simultaneous solution of the equations of motion of the fluid and shell coupled by boundary conditions at the shell surface. Though various approaches were considered in [1-3, 5, 6, 11, 13, 14, etc.] to solve this problem, no exact and complete results have been obtained yet.The findings in nonstationary elasticity and hydroelasticity are discussed in [14,16,18]. We will solve the problem on the basis of linear theory. Let the shell radius r 0 , the density of the fluid ρ 0 , and the sonic velocity in the fluid c 0 be units of measurement. Then all other quantities are measured in terms of fractions of the power complex r c 0 0 0 α β γ ρ that has the same dimension as a given quantity. With such an approach, all dependences will be dimensionless, which is convenient for theoretical analysis. We will describe the deformation of the shell using the linear theory of shells based on the Kirchhoff-Love hypothesis. Let the displacements of the shell's median surface, u, ν, and w, be the basic variables. Then, written in a cylindrical coordinate system x, r, θ whose axis coincides with the shell axis, the equations of motion of the shell take the following form [11]:
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.