Dichotomy property of dispersion equation of guided waves propagating in anisotropic composite plates

Accurate prediction of dispersion curves for ultrasonic guided waves propagation in multi layered composite laminates is crucial for the deployment of nondestructive testing procedures and structural health monitoring algorithms dedicated to aerospace composite materials. However, existing efforts mainly focused on finding ways to build complex-valued dispersion equations for guided waves (see transfer matrix method (TMM), global matrix method (GMM) and stiffness matrix method (SMM) for example) with little focus on developing efficient and stable numerical solving methods associated with the derived complex-valued equations. In this paper, the conditions under which complex-valued dispersion equations are either real or purely imaginary-valued equations (termed as dichotomy property) are derived for both single-and multi-layered composite plates. With such a property, the complex-valued dispersion equations can be efficiently numerically solved within the real number field via the standard bisection method or the corrected phase change method. It is thus now possible to overcome numerical issues frequently reported in literature. Besides, a parallel computing technique is proposed in this paper to improve the computational efficiency of the traditional GMM. The proposed methodology provides a new standard framework to solve the dispersion equations which is stable, multipurpose, and numerically efficient.