Motion of a compressible plate driven by shock or detonation

Abstract

The method of characteristics is used to obtain solutions for the time-dependent motion of a compressible plate driven by a one-dimensional shock or detonation followed by a constant state. The plate can either move in contact with or separate from the driver, depending on the values of the initial parameters. The motion of the surfaces is described by a system of linear, first-order, ordinary differential equations in one independent variable. The interior waves and interactions are determined from the surface motions. The equation of state of the plate has the form described by Murnaghan, specialized to produce straight characteristics in the x , t x,t plane. The equation of state for the driver is arbitrary. Closed-form solutions are obtained for the surfaces during their first reverberations for particular driver equations of state. Numerical examples are given which closely represent real systems. The results can be used as standards for finite-difference calculations.