Linear wave motions in continua with nano-pores

In the present investigation, the thermo-mechanical balance equations for a solid with nano-pores, viewed as a continuum with ellipsoidal microstructure, and the related conditions at a surface of discontinuity are stated. The appropriated constitutive relations for the linear theory are formulated. Then, the behavior of micro-vibrations, plane harmonic waves and macro-acceleration waves are analyzed: in the first case, three admissible modes are obtained; in the second instance, the dispersion relations gotten from the theory are solved by eight basic solutions; in the last one, all the velocities of propagation and the amplitudes of the discontinuity for either a heat-conducting or non-conducting material (corresponding, respectively, to isothermal and isentropic waves), as well as for generalized transverse waves are given. Furthermore, the growth equations which govern the propagation of the macro-acceleration waves and the couplings between the discontinuities are discussed.