Fast dispersion analysis of layered and periodic composite beams via a traction-continuity-preserving mixed finite element formulation

Dispersion analysis plays a crucial role in understanding wave propagation in composite beams, including both layered and axially jointed composite beams. Accurate characterization of interfacial traction continuity is essential for reliable dispersion prediction in composite structures. However, existing methods either lack cross-sectional flexibility or are based on displacement-only full-field finite elements, leading to high computational cost and limited accuracy at material interfaces. In this work, a state-space-based mixed finite element (MFE) formulation is developed for the dispersion analysis of layered and axially periodic composite beams. By treating displacements and stresses as independent variables, the proposed method preserves displacement compatibility and interface traction equilibrium within a unified mixed-field framework. Finite element discretization is performed only in the thickness direction, while the axial direction is handled through a state-space representation combined with differential quadrature and block-matrix condensation, transforming the dispersion analysis into a standard eigenvalue problem. This strategy avoids iterative frequency–wavenumber root searching and leads to a substantial reduction in computational cost compared with conventional finite element methods. Numerical examples demonstrate the accuracy and efficiency of the proposed method for both layered and axially periodic beams. Experimental tests on a sandwich composite beam are also carried out, providing additional validation of the theoretical predictions. Moreover, by explicitly accounting for traction continuity at material interfaces, we show that dispersion characteristics are influenced in a geometry-dependent manner—shifting upward for layered beams with interfaces parallel to the propagation direction, yet downward for periodic beams with interfaces normal to the propagation direction—an effect that has received little explicit attention in prior dispersion analyses. The proposed method offers an efficient framework and a new perspective for dispersion analysis of composite beam waveguides.