On Small-Displacement Waves in a Prestressed Body with Isotropic Incremental Elasticity Tensor

We consider a body at rest in a prestressed configuration κ which responds elastically to small incremental displacements from κ; the incremental elasticity tensor is assumed to be isotropic. On the basis of another paper [A. Montanaro, Internat. J. Non-Linear Mech. 33 (1998), no. 2, 327–355; MR1469859 (98f:73019)], we characterize the conditions for the propagation of longitudinal, transverse, and oblique small-displacement waves superimposed to κ. Formulae for the propagation speeds of these waves are written in terms of the prestress components and Lame parameters. The amplitudes of longitudinal and transverse waves are eigenvectors for the ´ prestress.