Elastodynamic reciprocity relations for wave scattering by flaws in fiber-reinforced composite plates

Due to light weight, high performance and increased service life, fiber-reinforced composite materials are receiving wide attention as an advanced material in many branches of engineering. Structural integrity of composite structures is affected by the presence of flaws such as cracks and delaminations in the composite material. In this paper, elastodynamic reciprocity relations are developed for wave scattering by flaws when guided waves are allowed to propagate in fiber-reinforced composite plates. These relations are useful to check the accuracy of the numerical solution for the scattered wave field in ultrasonic non-destructive evaluation of flaws in composite plate-like structural elements. The classical elastodynamic reciprocity theorem is used to derive simple reciprocity relations for reflected and transmitted wave amplitudes and the corresponding energies associated with the wave modes in a plate with an arbitrary stacking sequence. The derived reciprocity relations are used to check the accuracy of the numerical solution for several example scattering problems.