Steady Shock Profile in a One‐Dimensional Lattice
作者:
George E. Duvall,
R. Manvi,
Sherman C. Lowell,
期刊:
Journal of Applied Physics
(AIP Available online 1969)
卷期:
Volume 40,
issue 9
页码: 3771-3775
ISSN:0021-8979
年代: 1969
DOI:10.1063/1.1658270
出版商: AIP
数据来源: AIP
摘要:
The equations of motion of a one‐dimensional lattice of mass points connected by nonlinear springs are set forth and compared with the equations of the corresponding continuum. A permanent regime for the damped lattice is obtained by series approximation and shown to agree with that of the continuum. A higher approximation leads to a permanent regime profile for the undamped lattice which oscillates steadily after shock arrival. This is shown to be in qualitative accord with the results of numerical integrations of the transient problem. However, comparison of periods of steady oscillation with those obtained in the transient problem indicate that the series approximation to the permanent regime is quantitatively unsatisfactory, though qualitatively correct. Scaling of the problem with a parameteru1&agr; is noted, whereu1is steady particle velocity behind the shock and &agr; is a parameter of nonlinearity.
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