Transport Equation for Shock Strenght in Hyperelastic Rods
The singular surface theory and perturbation method of solution are used to examine a 1–D shock wave propagation problem in a semi-infinite rod of slowly varying cross-sectional area. The isentropic approximation is used. The weak nonlinear shock propagates into a region, which is homogeneously deformed and at rest. A numerical analysis for decreasing and increasing cross-sectional areas, and for a special type of nonlinear elastic material is conducted.
Y.B. FU and N.H. SCOTT, The evolution law of one-dimensional weak nonlinear shock waves in elastic non-conductors, Q.J. Mech. Appl. Math., 42, pp. 23-39, 1989.
Y.B. FU and N.H. SCOTT, Propagation of simple waves and shock waves in a rod of slowly varying cross-sectional area, Int. J. Engng. Sci., 32, 1, pp. 35-44, 1994.
A. JEFFREY, Acceleration wave propagation in hyperelastic rods of variable crosssection, Wave Motion, 4, pp.173-180, 1982.
P.J. CHEN, One-dimensional shock waves in elastic non-conductors, ARMA1 43, pp. 350-362, 1971.
S. KOSIŃSKI, Plane shock wave in initially deformed elastic material [in Polish], Mech. Teor. Stos., 19, 4, 545-562, 1981.
Z. WESOŁOWSKI, Strong discontinuity wave in initially strained elastic medium, Arch. Mech., 30, 3, 309-322, 1978.
H.B. DWIGHT, Tables of integrals and other mathematical data, Macmillan, New York 1961.
USER'S GUIDE Mathcad 5.0+ for Windows, Math. Soft. Inc., 1994.
Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland