Variable-kinematics finite elements for propagation analyses of two-dimensional waveguides

This paper introduces advanced kinematics plate and shell models for evaluating the dispersion characteristics of two-dimensional waveguides. The models utilize high-order functions to interpolate primary variables across the waveguide, both in thickness and above its plane. Specifically, Taylor and Lagrange expansions are employed to describe thickness deformation, while Lagrangian shape functions approximate the displacement field along the propagation directions. The Carrera Unified Formulation is adopted to derive stiffness and mass matrices corresponding to various structural theories. These matrices are subsequently post-processed according to the Wave Finite Element Method to construct the transfer matrix of a representative waveguide segment, enabling the extraction of dispersion properties from its eigenvalues. The proposed methodology, employing variable-fidelity finite elements, is validated using thin, thick plates and shells composed of isotropic or orthotropic materials. The obtained results are compared against numerical and analytical solutions available in the existing literature.