Motion of a compressible plate driven by shock or detonation
Authors:
W. C. Rivard and Ray Engelke
Journal:
Quart. Appl. Math. 32 (1974), 29-43
DOI:
https://doi.org/10.1090/qam/99689
MathSciNet review:
QAM99689
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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 $x,t$ 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.
- Francis D. Murnaghan, Finite deformation of an elastic solid, John Wiley & Sons, Inc., New York, N. Y.; Chapman & Hall, Ltd., London, 1951. MR 0045548
D. C. Pack, The reflection and transmission of shock waves, Phil. Mag. 2, 182–195 (1957)
A. K. Aziz, H. Hurwitz, and H. M. Sternberg, Energy transfer to a rigid piston under detonation loading, in Proceedings Third Symposium on Detonation (Princeton Univ., 1960) ONR Symp. Rpt. ACR-52, Vol. 1, pp. 205–225
Y. Kivity and A. Kogan, Analytical solution of the flow field produced by the impact of finite plates, Israel J. Tech. 7, 457–464 (1969)
- C. M. Ablow, Wave refraction at an interface, Quart. Appl. Math. 18 (1960/61), 15–29. MR 135022, DOI https://doi.org/10.1090/S0033-569X-1960-0135022-3
W. Fickett, Motion of an explosive-induced plane shock wave, Quart. Appl. Math., this issue
Y. Kivity and A. Kogan, Interaction at the interface of two colliding plates, Israel J. Tech. 8, 325–328 (1970)
- R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, Interscience Publishers, Inc., New York, N. Y., 1948. MR 0029615
J. M. Walsh, M. H. Rice, R. G. McQueen, and F. L. Yarger, Shock-wave compressions of twenty-seven metals: equations of state of metals, Phys. Rev. 108, 196–216 (1957)
Group GMX-6, Los Alamos Scientific Laboratory, Selected Hugoniots, Report LA-4167-MS, 1969
W. E. Deal, Measurement of the reflected shock Hugoniot and isentrope for explosive reaction products, Phys. Fluids 1, 523–527 (1958)
F. D. Murnaghan, Finite deformation of an elastic solid, Wiley, New York, 1951, pp. 71–79
D. C. Pack, The reflection and transmission of shock waves, Phil. Mag. 2, 182–195 (1957)
A. K. Aziz, H. Hurwitz, and H. M. Sternberg, Energy transfer to a rigid piston under detonation loading, in Proceedings Third Symposium on Detonation (Princeton Univ., 1960) ONR Symp. Rpt. ACR-52, Vol. 1, pp. 205–225
Y. Kivity and A. Kogan, Analytical solution of the flow field produced by the impact of finite plates, Israel J. Tech. 7, 457–464 (1969)
C. M. Ablow, Wave refraction at an interface, Quart. Appl. Math. 18, 15–29 (1960)
W. Fickett, Motion of an explosive-induced plane shock wave, Quart. Appl. Math., this issue
Y. Kivity and A. Kogan, Interaction at the interface of two colliding plates, Israel J. Tech. 8, 325–328 (1970)
R. Courant and K. O. Friedrichs, Supersonic flow and shock waves, Interscience, New York, 1948
J. M. Walsh, M. H. Rice, R. G. McQueen, and F. L. Yarger, Shock-wave compressions of twenty-seven metals: equations of state of metals, Phys. Rev. 108, 196–216 (1957)
Group GMX-6, Los Alamos Scientific Laboratory, Selected Hugoniots, Report LA-4167-MS, 1969
W. E. Deal, Measurement of the reflected shock Hugoniot and isentrope for explosive reaction products, Phys. Fluids 1, 523–527 (1958)
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Article copyright:
© Copyright 1974
American Mathematical Society
