Non-linear interaction of waves in prestressed material

Interaction of two counterpropagating ultrasonic waves in an inhomogeneously prestressed elastic material (a structural element) with quadratic non-linearity is studied theoretically by using the perturbative formalism. The analytical solution that describes wave–wave, wave–material and wave–prestress non-linear interaction is derived. This rather cumbersome solution is studied in the case of a harmonic boundary condition in the material (specimen) subjected to two-parametric inhomogeneous prestressed state. The model problems are solved and the influence of the prestress on the wave interaction is cleared up. Resulting oscillations on two parallel boundaries of the material are prestress sensitive. It is proposed to use boundary oscillation data for non-destructive characterization of inhomogeneous prestressed state.