Continuation Approach Combined with Semi-Analytical Finite-Element Method for Solving Guided-Wave Dispersion Equation

Abstract The present article introduces a tracing algorithm for dispersion curves for guided waves. The quadratic eigenvalue problem for dispersion analysis is constructed in a semi-analytical finite-element model. The eigenvalue problem is converted into a system of nonlinear equations by introducing phase and amplitude conditions for the eigenvector. Solutions of the system of nonlinear equations are traced by means of a numerical continuation method (NCM). The proximity of dispersion curves, which is referred to as mode veering, becomes a problem in the NCM tracing process. In order to overcome the mode-veering issue, constraints on the tangential and curvature vectors for the dispersion curve are proposed. Several numerical results demonstrate that the proposed NCM can trace dispersion curves appropriately, even for mode-veering cases. Furthermore, the group velocities of guided waves can be calculated easily and accurately in the proposed formulation.