High-order finite beam elements for propagation analyses of arbitrary-shaped one-dimensional waveguides

This paper presents advanced-kinematics beam models to compute the dispersion characteristics of one-dimensional guides. High-order functions are used to interpolate the primary variables above the waveguide cross-section and along its axis. Taylor- and Lagrange-type bi-dimensional expansions are employed to describe the section deformation, while Lagrangian shape functions approximate the displacement field along the propagating direction. According to the Wave Finite Element Method, the stiffness and mass matrices corresponding to various structural theories are post-processed to build the transfer matrix of a representative waveguide portion. The Carrera Unified Formulation is exploited to calculate these matrices.