Acoustoelastic Effects in Elastic Media with Nonuniform Initial Stress

A perturbative formalism for the treatment of the acoustoelastic effect in material plates with a stress profile in the thickness direction is proposed and compared with a numerical method. The latter consists of an application of the local interaction simulation approach (LISA). The reliability of both the analytical treatment and the numerical approach is tested by comparing the respective results for several cases of propagation of Rayleigh waves in specimens with various kinds of stress fields, including welded steel plates. Finally, the linearization obtained from the perturbation treatment is exploited for the solution of the ``inverse problem,'' i.e., the determination of the stress field from a set of RW times of flight with different wavelengths. A numerical example is provided to illustrate the applicability of the method, starting from a set of synthetic data obtained with LISA.