ABSTRACT
The elastodynamic governing equations (4.33) and (4.34) represent a coupled system of partial differential equations of first order for the field quantities v(R, t) and T(R, t) after introducing constitutive equations of linear time invariant instantaneously and locally reacting materials, that are always considered in this section. To neutralize this coupling in terms of a decoupling both equations are inserted into each other: We obtain partial differential equations of second order either for v(R, t) or for T(R, t). Since both equations allow for waves as solutions, we generally call them “wave equations” even though they are more complicated than the simple d’Alembert wave equation (5.32), hence the terminology “Navier wave equations” is sometimes used in the literature. Another decoupling method, even though valid only for homogeneous isotropic materials, is dealt with in connection with the Helmholtz decomposition of a vector into potentials.
