Wave Propagation

Abstract

A review of the method of characteristics applied to the theory of stress waves in solids has been given by Hopkins [23]. The governing equations considered are of the form

$$$$

(2.1.1)

where the coefficients a _ij , b _ij and c _i are in general functions of the independent variables (x, t) and of then dependent variables u _j ; the repeated (dummy) suffix j implies summation over the values j = 1, 2,..., n. It is found that there are curves C in the (x, t) plane across which there may be discontinuities in the first derivatives of u _i . These curves are given by

$$$$

(2.1.2)

where the values of λ _v are the roots of

$$$$

(2.1.3)