A General Tensorial Formulation of Acoustoelasticity and Its Representation in Cylindrical Coordinates

Acoustoelasticity describes the relationship between elastic wave velocities and the initial stress present in media. Most of the current research in this area is focused on elastic waves propagating in naturally isotropic media with initially uniaxial stress and confined the solution of acoustoelastic problem to the Cartesian coordinate system, which limits the application for the acoustoelasticity theory. In this paper, to make up for this deficiency, an acoustoelastic formulation, i.e. the equation of motion for incremental displacement with explicit dependency on initial stress or strain, is developed based on the general theory of incremental deformation. This formulation can be applied to material with any symmetricity, initial stress with any number of principle axis. Also, it can be expressed in any form of coordinate system for its tensorial nature. Furthermore, to the knowledge of authors, there is no integrated cylindrical expression for acoustoelastic theory, an expansion of the formulation in a cylindrical system for an orthotropic material is given in detail for the convenience of application, such as cylindrical waves.