A wavenumber dynamic stiffness method for exact and efficient dispersion analysis of plate built-up waveguides

This paper proposes an efficient wavenumber dynamic stiffness method (WDSM) for exact dispersion analysis of plate built-up waveguides. Firstly, the wavenumber dynamic stiffness (WDS) matrices for inplane and out-of-plane wave motions of a plate waveguide element are developed by using the general solutions of the governing differential equations as the exact shape functions. The Wittrick–Williams (WW) algorithm is used as the eigen-solution technique to calculate dispersion relations. Furthermore, the explicit expression for the $J_0$ term in the WW algorithm is derived, which enables the proposed method to conduct dispersion analysis of complex plate built-up waveguides with very few elements and eliminates the need for mesh refinement throughout the entire frequency range. The proposed WDSM is then applied to several examples including individual plate strip and complex plate built-up waveguides. Results are compared with existing exact solutions and those obtained by using the wave finite element method (WFEM) and the semi-analytical finite element method (SAFEM), which demonstrate the exactness and the significantly improved computational efficiency of the proposed WDSM. In conclusion, this paper presents an exact and efficient dispersion analysis method for complex plate built-up waveguides, which can be considered as a competitive alternative to numerical methods such as SAFEM and WFEM.