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.