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Towards an Unified Approach for Guided Ultrasonic Wave Dispersion Curves in Metallic and Composites Materials



In current literature, algorithms for predicting guided ultrasonic wave dispersion curves use different solution approaches based on the material type of the medium in which the waves propagate, thereby distinguishing between isotropic and anisotropic material. For composites which have a slight degree of anisotropy, however, both solution approaches are not satisfactory. This manuscript, therefore, proposes an unified approach which is valid for any material regardless its degree of anisotropy. The proposed unified approach was based on the eigenvalue problem which was derived from the Christoffel equation for a lamina. The eigenvalues, and eigenvectors were obtained straightforward by solving the eigenvalue problem. Special attention, however, was required when identify the polarization of the eigenvectors, and ensuring continuity within a set of eigenvectors when transiting from complex to real roots as result of the Christoffel equation. The traction free boundary conditions were applied to set up the six by six stress-displacement matrix which was solved to find the wavenumber-velocity pairs which yielded a solution. As result of using the Christoffel equation, a complex determinant for each wavenumber-velocity pair was obtained. A simple, and elegant ap- proach, based on the phase between succeeding velocities for a fixed wavenumber, was developed, and applied successfully to determine the wavenumber-velocity pairs which yielded a solution. The proposed unified approach was evaluated for both isotropic, and anisotropic materials. The developed algorithm verified using the commercially available software package DISPERSE.

doi: 10.12783/SHM2015/220

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