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Non-linear interaction of waves in prestressed material
Authors:A Ravasoo  
Institution:

aCentre for Nonlinear Studies, Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn, Estonia

Abstract: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.
Keywords:Ultrasonic waves  Non-linear interaction  Non-linear elastic material  Inhomogeneous prestress  Non-destructive prestress characterization
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