ENERGY-BALANCE AND FUNDAMENTAL RELATIONS IN ANISOTROPIC-VISCOELASTIC MEDIA

The first part of this work analyses the energy balance equation for i nhomogeneous time-harmonic waves propagating in a linear anisotropic-v iscoelastic medium whose constitutive equation is described by a gener al time-dependent relaxation matrix of 21 independent components. This matrix includes most linear anisotropic-viscoelastic theologies and t he generalized Hooke's law. The balance of energy allows the identific ation of the potential and loss energy densities, which are related to the real and imaginary parts of the complex stiffness matrix. The sec ond part establishes some fundamental relations valid for inhomogeneou s viscoelastic plane waves. The scalar product between the complex wav enumber and the complex power flow vector is a real quantity proportio nal to the time-average kinetic energy density. As in the anisotropic- elastic case, it is confirmed that the phase velocity is the projectio n of the energy velocity vector onto the propagation direction. A simi lar equation is obtained by replacing the energy velocity with a veloc ity related to the dissipated energy. Finally, as in isotropic-viscoel astic media, the time-average energy density can be obtained from the projection of the average power flow vector onto the propagation direc tion, and the time-average dissipated energy density from the projecti on of the average power flow vector onto the attenuation direction.