On the first—order speeds in any directions of acceleration waves in prestressed second—order isotropic, compressible, and homogeneous materials

In this paper, using the perturbation method we proposed in [A. Marasco, A. Romano, On the ordinary waves in second-order elastic, isotropic, compressible, and homogeneous materials, Math. Comput. Modelling 49 (7-8) (2009) 1504-1518], the first–order terms of the speeds and the amplitude of the principal waves and of the waves in any propagation direction are determined in second–order elastic, isotropic, compressible, and homogeneous materials. Moreover, for the general waves we determine the relations among the second–order constitutive constants which ensure that the waves are longitudinal or transverse.