SHOCK WAVE PROPAGATION IN A DISSIPATING LATTICE MODEL.
WASHINGTON STATE UNIV PULLMAN SHOCK DYNAMICS LAB
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A model for one dimensional shock wave propagation is studied. The model consists of a semi-infinite chain of particles with nonlinear nearest neighbor interaction. The nonlinear force law for springs considered in the study is of parabolic and Morse type. The viscosity is introduced for dissipation by means of a mechanical dashpot in parallel with the spring. The resulting differential-difference equation of motion is numerically integrated by an iterative scheme on the IBM 36067 computer. The object of the study is to show the analogy between the lattice model and the continuum for shock wave propagation. It is found that viscosity as introduced in the model plays an important role in the structure and propagation mode of the shock wave. An attempt is also made for the analytic solution of the nonlinear differential-difference equation of motion under reasonable simplifications as a check on the computer solution and for better understanding of the physics of the problem.