Estimation of dispersion curves by combining effective elastic constants and SAFE method: a case study in a plate under stress

Abstract

This paper presents an approach to calculate dispersion curves for homogeneous and isotropic plates subject to stress, via Semi-Analytical Finite Element and the Effective Elastic Constants, since stresses in the waveguide modify the phase and group velocities of the lamb waves. In the proposed methodology an isotropic specimen subjected to anisotropic loading is emulated by proposing an equivalent stress-free anisotropic specimen. This approximation facilitates determining the dispersion curves by using the well-studied numerical solution for the stress-free cases. The lamb wave in anisotropic materials can be studied by means of the Effective Elastic Constants, which reduces the complexity of the numerical implementation. Finally, numerical data available in literature were used to validate the proposed methodology, where it could be demonstrated its effectiveness as approximated method.