Interaction of Bursts as a Detector of Material Inhomogeneity

Abstract

The nonlinear propagation and interaction of one-dimensional counterpropagating harmonic bursts in the elastic material is studied on the basis of the fivec onstant nonlinear theory of elasticity.T he proper choice of bursts parameters leads to the effect by which the oscillations evoked by counterpropagating bursts in the homogeneous material disappear.This effect facilitates qualitative nondestructive determination of the inhomogeneity in material properties. The results of numerical simulations illustrate this possibility for the exponentially graded materials.

Wave equations in mechanics

“…(15) is pretty complicated, it is possible to solve it by perturbation techniques provided the space-dependence is weak [ 21 ].…”

“…The possible nonlinear modifications of Eqs (20) and (21) are given by Engelbrecht [ 11 ]. The kernel of the convolution integral in Eqs (20) and (21) corresponds to the standard viscoelastic model [ 22 ], which models both dispersion and relaxation effects.…”