A unified formulation for predictive modeling of guided-ultrasonic wave dispersion curves in metallic and composite materials

Abstract

To predict dispersion curves it is common to use different solution approaches depending on the material type, isotropic or composite, of the medium in which the wave propagates. The two different solution methods are defined in different domains, frequency–wavespeed domain for isotropic materials, and wavenumber–wavespeed domain for composites which can lead to difficulties, and unsatisfying results when predicting the dispersion curves for hybrid laminates which contain both isotropic and composite materials. This article, therefore, proposes a unified formulation defined in the wavenumber–wavespeed domain for both isotropic and composite materials. The unified formulation, simple, and mathematically straightforward formulation, utilizes Christoffel’s equation for a lamina to obtain the eigenvalues and eigenvectors. The eigenvalues and eigenvectors are then used to set up the field matrix from which the dispersion curves could be retrieved. Once the dispersion curves were obtained the waves are grouped using a modeshape analysis. A spline algorithm is applied to obtain a continuous solution from a rough domain which was used to reduce computational time. In addition, this article highlights the challenges faced in the numerical process, and provides a discussions of the methods used to overcome these obstacles.