A mathematical model for small elastic disturbances propagation in strained solid continuum

A mathematical model for the propagation of small elastic disturbances in a strained solid continuum is considered. The model is based on assumptions about the dependence of the acoustic parameters of the continuum on the initial strains. The model includes a system of hyperbolic partial differential equations, coefficients of which are dependent on the strain components. An iterative approach for solving this system of equations with specially dependent coefficients is developed. The approach enables taking into account, in the zero approximation, the influence of the integral parameters of the initial strain distribution on the elastic disturbance. Possibilities of utilizing the mathematical model to formulate the inverse problems of restorating the strain and stress fields are discussed