Trade-off between ordinary differential equation and Legendre polynomial methods to study guided modes in angle-ply laminate

Abstract

It has been shown that the roots of guided waves in laminate plates produced by the ordinary differential equations (ODE) approach may not hold under to some computational conditions. A particular drawback of the 2D formulation of the ODE approach is the lack of reliability in the case of unidirectional laminates due to the decoupling properties between the SH and Lamb wave modes, which is caused by the unified matrix of roots. Due to this problem, the SH modes disappear from the unified roots of guided modes, then re-emerge with a separate computation of the SH and Lamb wave modes. Initially, we did not notice this computational “bug” in the event of a coupling between the SH and Lamb wave modes. In this context, the Legendre polynomial method is used to illustrate that fact. Results demonstrate how the polynomial method is pre-eminent to handle the laminate modelling over the ODE method for these specific requirements, however, a trade-off between these two methods needs to be considered to obtain stable and robust behavior of guided dispersion curves. This short study ends with conclusions and future perspectives.